Mathematics

• Introductory Module: Numerical Mathematics III

  0280cA1.12
  • 19215201 Lecture
    Basic Module: Numerics III (Volker John)
    Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisites

    Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

    Comments

    The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

     

    Suggested reading

    • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
    • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)

  • 19215202 Practice seminar
    Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
    Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Homepage:Wiki der Numerik II

• Introductory Module: Partial Differential Equations I

  0280cA1.13
  • 19241301 Lecture
    Partial Differential Equations I (André Erhardt)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Comments

    • Basic differential equations (Laplace,- heat and wave equations)
    • Representation formulas
    • Solution methods
    • Introduction to Hilbert space methods

    This can serve as the basis for a BSc and/or MSc project.  

    Suggested reading

    L.C. Evans, Partial Differential Equations
     

  • 19241302 Practice seminar
    Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
    Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    

• Introductory Module: Topology I

  0280cA1.17
  • 19205401 Lecture
    Basic module: Topology I (Christian Haase)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    
    Course Overview This is a beginning course from the series of three courses Topology I—III:

    1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
    2. Groups acting on topological spaces
    3. Gluing constructions, simplicial complexes
    4. Homotopies between continuous maps, degree of a map, fundamental group.
    5. Seifert-van Kampen Theorem.
    6. Covering spaces.
    7. Simplicial homology
    8. Combinatorial applications

    Suggested reading

    Literature:

    1. M. A. Armstron: Basic Topology, Springer UTM
    2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
    3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
    4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
    5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
    6. Klaus Jänich: Topologie, Springer-Verlag
    7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
    8. James R. Munkres: Topology, Prentice Hall

  • 19205402 Practice seminar
    Exercise for Basic Module: Topology I (Sofia Garzón Mora)
    Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

• Introductory Module: Algebra II

  0280cA1.2
  • 19214501 Lecture
    Basic Module: Algebra II (Holger Reich)
    Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisits: Comutitive algebra

    Comments

    The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

    Possible topics include: 
    - categories and functors
    - additive and abelian categories
    - cohomology
    - sheaf theory
    - ringed spaces
    - schemes
    - separated and proper morphisms
    - blowing up
    - embeddings into projective spaces, divisors, invertible sheaves 
    - Riemann-Roch -Gröbner bases.

    Suggested reading

    For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten

  • 19214502 Practice seminar
    Practice seminar for Basic Module: Algebra II (Georg Lehner)
    Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Introductory Module: Discrete Geometry II

  0280cA1.6
  • 19214901 Lecture
    Basic Module: Discrete Geometrie II (Georg Loho)
    Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

    Comments

    Inhalt:

    This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

    The material will be a selection of the following topics:
    Linear programming and some applications

     

    • Linear programming and duality
    • Pivot rules and the diameter of polytopes

    Subdivisions and triangulations

    • Delaunay and Voronoi
    • Delaunay triangulations and inscribable polytopes
    • Weighted Voronoi diagrams and optimal transport

    Basic structures in convex geometry

     

    • convexity and separation theorems
    • convex bodies and polytopes/polyhedra
    • polarity
    • Mahler’s conjecture
    • approximation by polytopes

    Volumes and roundness

    • Hilbert’s third problem
    • volumes and mixed volumes
    • volume computations and estimates
    • Löwner-John ellipsoids and roundness
    • valuations

    Geometric inequalities

    • Brunn-Minkowski and Alexandrov-Fenchel inequality
    • isoperimetric inequalities
    • measure concentration and phenomena in high-dimensions

    Geometry of numbers

    • lattices
    • Minkowski's (first) theorem
    • successive minima
    • lattice points in convex bodies and Ehrhart's theorem
    • Ehrhart-Macdonald reciprocity

    Sphere packings

    • lattice packings and coverings
    • the Theorem of Minkowski-Hlawka
    • analytic methods

    Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

    Suggested reading

    The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.

  • 19214902 Practice seminar
    Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Introductory Module: Discrete Mathematics I

  0280cA1.7
  • 19214701 Lecture
    Discrete Mathematics I (Ralf Borndörfer)
    Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Target group:

    BMS students, Master and Bachelor students

    Whiteboard:

    You need access to the whiteboard in order to receive information and participate in the exercises.

    Large tutorial:

    Participation is recommended, but non-mandatory.

    Exams:

    1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
    2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

    Comments

    Content:

    Selection from the following topics:

    • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)

    Suggested reading

    • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
    • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
    • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
    • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
    • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.

  • 19214702 Practice seminar
    Practice seminar for Discrete Mathematics I (Silas Rathke)
    Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Comments

    Content:

    Selection from the following topics:

    • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)
    • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)

• Introductory Module: Dynamical Systems I

  0280cA1.9
  • 19215601 Lecture Cancelled
    Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

    Comments

    Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

    Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

    Suggested reading

    L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

    Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).

  • 19215602 Practice seminar Cancelled
    Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Am 23. April findet keine Übung statt.

• Advanced Module: Discrete Mathematics III

  0280cA2.4
  • 19215001 Lecture
    Constructive Combinatorics (Tibor Szabo)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Basic Bachelor Algebra, Probability, and Disrete Mathematics.

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

    Suggested reading

    A script will be provided.

  • 19215002 Practice seminar
    Constructive Combinatorics exercises (Tibor Szabo)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

• Advanced Module: Numerical Mathematics IV

  0280cA2.6
  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

    Requirements: basic courses in analysis, basic course numerical mathematics

    Literature:

    Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
    https://doi.org/10.3390/atmos14101523

    T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

    J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

    Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000

  • 19215301 Lecture
    Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Content:

    Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

    Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

     

    This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

    The course will cover a selection from the following topics

    1. Conservation laws and governing equations,

    2. Numerical methods for geophysical flow simulations,

    3. Dynamical systems and bifurcation theory,

    4. Data-based characterization of atmospheric flows

     

    This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

    Suggested reading

    Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

    Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

     

  • 19222601 Lecture
    Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Zielgruppe: Students who are interested in stochastics and numerics
    Voraussetzungen: Stochastik I + II, Numerik I + II

    Comments

    Inhalt der Veranstaltung:
    The lecture will cover the following topics (not exhaustive)

    • Brownian motion 
    • Numerical discretization of stochastic differential equations
    • Monte Carlo methods
    • Representations of random fields
    • Modelling with stochastic differential equations
    • Applications

    Suggested reading

    Literatur:

    1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
    2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
    3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
    4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
    5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014

  • 19223901 Lecture
    Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
    Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

    Suggested reading

    The following books will be relevant:

    • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
    • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
    • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
    • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.

  • 19234501 Lecture
    Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: T9/053 Seminarraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of stochastics, and numerical methods

    Comments

    Content:

    Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

    - Basic of stochastic processes:

    Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

    - Model reduction techniques for stochastic dynamics:

    averaging technique, effective dynamics, Markov state modeling

    - Machine learning techniques using/for stochastic dynamics: 

    dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

    Suggested reading

    1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

    2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

    3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

    4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

    5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

    6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.

  • 19207102 Practice seminar
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19215302 Practice seminar
    Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    
  • 19222602 Practice seminar
    Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19223902 Practice seminar
    Übung zu UQ and QMC (Claudia Schillings)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19234502 Practice seminar
    Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

• Advanced Module: Partial Differential Equations III

  0280cA2.7
  • 19243001 Lecture
    Partial Differential Equations III (Erica Ipocoana)
    Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Voraussetzungen: Partielle Differentialgleichungen I und II

    Comments

    The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

     

    Suggested reading

    Wird in der Vorlesung bekannt gegeben / to be announced.

  • 19243002 Practice seminar
    Tutorial Partial Differential Equations III (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
    Location: A3/SR 119 (Arnimallee 3-5)
    

• Advanced Module: Probability and Statistics IV

  0280cA2.8
  • 19222601 Lecture
    Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Zielgruppe: Students who are interested in stochastics and numerics
    Voraussetzungen: Stochastik I + II, Numerik I + II

    Comments

    Inhalt der Veranstaltung:
    The lecture will cover the following topics (not exhaustive)

    • Brownian motion 
    • Numerical discretization of stochastic differential equations
    • Monte Carlo methods
    • Representations of random fields
    • Modelling with stochastic differential equations
    • Applications

    Suggested reading

    Literatur:

    1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
    2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
    3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
    4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
    5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014

  • 19229601 Lecture Cancelled
    Stochastic dynamics in fluids (Felix Höfling)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Target audience: M.Sc. Computational Sciences/Mathematik/Physik

    Requirements: some advanced course on either statistical physics or stochastic processes

    Comments

    The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

    The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

    Keywords:

    • Brownian motion, diffusion, and stochastic processes in fluids
    • harmonic analysis of correlation functions
    • Zwanzig-Mori projection operator formalism
    • mode-coupling approximations, long-time tails
    • critical dynamics and transport anomalies

    Suggested reading

    • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
    • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

    Further literature will be given during the course.

  • 19242101 Lecture
    Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I, II, III. 
    Recommended: Functional Analysis.

    Comments

    Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

    • Ito calculus for Gaussian random measures;
    • semilinear stochastic PDEs in one dimension;
    • Schauder estimates;
    • Gaussian hypercontractivity;
    • paraproducts and paracontrolled distributions;
    • local existence and uniqueness for semilinear SPDEs in higher dimensions;
    • properties of solutions

    Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

    Suggested reading

    Literature
    There will be lecture notes.

  • 19222602 Practice seminar
    Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19229602 Practice seminar Cancelled
    Exercises to Stochastic processes in fluids (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19242102 Practice seminar
    Exercise: Stochastics IV (Guilherme de Lima Feltes)
    Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

• Specialization Module: Master's Seminar on Discrete Mathematics

  0280cA3.4
  • 19206011 Seminar
    Discrete Mathematics Masterseminar (Tibor Szabo)
    Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

     

     

    Comments

    Content:
    The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
    Target audience:
    BMS students, Master students, or advanced Bachelor students.
    Prerequisites:
    Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

     

• Specialization Module: Master’s Seminar on Numerical Mathematics

  0280cA3.6
  • 19226611 Seminar
    Seminar Quantum Computational Methods (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

    Comments

    The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
    In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
    Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

    Suggested reading

    Related Basic Literature:
    (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
    (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
    (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871

  • 19227611 Seminar
    Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Comments

    The seminar covers advanced topics of uncertainty quantification and inverse problems.

• Specialization Module: Master's Seminar on Partial Differential Equations

  0280cA3.7
  • 19247111 Seminar
    Variational methods & Gamma-convergence (Marita Thomas)
    Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

• Specialization Module: Master’s Seminar on Topology

  0280cA3.9
  • 19233511 Seminar
    Geometric Group Theory (Georg Lehner)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Additional information / Pre-requisites

    Aimed at: Bachelor and masters students
    
    Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.

    Comments

    Groups are best understood as symmetries of mathematical objects. Whereas finite groups can often be completely understood by their actions on vector spaces, this approach will often fail with infinite groups, such as free groups or hyperbolic groups. Geometric group theory tries to construct natural geometric objects (topological spaces such as manifolds or graphs for example) that these groups act on and allows one to classify the complexity these groups can have.
    
    In this seminar, we will follow Clara Löh's book on the subject. Topics will include Cayley graphs, free groups and their subgroups, quasi-isometry classes of groups, growth types of groups, hyperbolic groups and the Banach-Tarski theorem.

    Suggested reading

    Clara Löh - Geometric Group Theory

• Complementary Module: Selected Topics A

  0280cA4.1
  • 19205401 Lecture
    Basic module: Topology I (Christian Haase)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    
    Course Overview This is a beginning course from the series of three courses Topology I—III:

    1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
    2. Groups acting on topological spaces
    3. Gluing constructions, simplicial complexes
    4. Homotopies between continuous maps, degree of a map, fundamental group.
    5. Seifert-van Kampen Theorem.
    6. Covering spaces.
    7. Simplicial homology
    8. Combinatorial applications

    Suggested reading

    Literature:

    1. M. A. Armstron: Basic Topology, Springer UTM
    2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
    3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
    4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
    5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
    6. Klaus Jänich: Topologie, Springer-Verlag
    7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
    8. James R. Munkres: Topology, Prentice Hall

  • 19214501 Lecture
    Basic Module: Algebra II (Holger Reich)
    Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisits: Comutitive algebra

    Comments

    The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

    Possible topics include: 
    - categories and functors
    - additive and abelian categories
    - cohomology
    - sheaf theory
    - ringed spaces
    - schemes
    - separated and proper morphisms
    - blowing up
    - embeddings into projective spaces, divisors, invertible sheaves 
    - Riemann-Roch -Gröbner bases.

    Suggested reading

    For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten

  • 19214701 Lecture
    Discrete Mathematics I (Ralf Borndörfer)
    Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Target group:

    BMS students, Master and Bachelor students

    Whiteboard:

    You need access to the whiteboard in order to receive information and participate in the exercises.

    Large tutorial:

    Participation is recommended, but non-mandatory.

    Exams:

    1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
    2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

    Comments

    Content:

    Selection from the following topics:

    • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)

    Suggested reading

    • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
    • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
    • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
    • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
    • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.

  • 19214901 Lecture
    Basic Module: Discrete Geometrie II (Georg Loho)
    Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

    Comments

    Inhalt:

    This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

    The material will be a selection of the following topics:
    Linear programming and some applications

     

    • Linear programming and duality
    • Pivot rules and the diameter of polytopes

    Subdivisions and triangulations

    • Delaunay and Voronoi
    • Delaunay triangulations and inscribable polytopes
    • Weighted Voronoi diagrams and optimal transport

    Basic structures in convex geometry

     

    • convexity and separation theorems
    • convex bodies and polytopes/polyhedra
    • polarity
    • Mahler’s conjecture
    • approximation by polytopes

    Volumes and roundness

    • Hilbert’s third problem
    • volumes and mixed volumes
    • volume computations and estimates
    • Löwner-John ellipsoids and roundness
    • valuations

    Geometric inequalities

    • Brunn-Minkowski and Alexandrov-Fenchel inequality
    • isoperimetric inequalities
    • measure concentration and phenomena in high-dimensions

    Geometry of numbers

    • lattices
    • Minkowski's (first) theorem
    • successive minima
    • lattice points in convex bodies and Ehrhart's theorem
    • Ehrhart-Macdonald reciprocity

    Sphere packings

    • lattice packings and coverings
    • the Theorem of Minkowski-Hlawka
    • analytic methods

    Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

    Suggested reading

    The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.

  • 19215201 Lecture
    Basic Module: Numerics III (Volker John)
    Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisites

    Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

    Comments

    The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

     

    Suggested reading

    • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
    • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)

  • 19215601 Lecture Cancelled
    Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

    Comments

    Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

    Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

    Suggested reading

    L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

    Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).

  • 19241301 Lecture
    Partial Differential Equations I (André Erhardt)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Comments

    • Basic differential equations (Laplace,- heat and wave equations)
    • Representation formulas
    • Solution methods
    • Introduction to Hilbert space methods

    This can serve as the basis for a BSc and/or MSc project.  

    Suggested reading

    L.C. Evans, Partial Differential Equations
     

  • 19248101 Lecture
    Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
     

    Leitidee der Veranstaltung
    Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

    Inhaltliche Schwerpunkte
    Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

    Methodische Konzeption
    Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

    Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
    Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

    Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
     

    Überblick über die wöchentliche Struktur der Veranstaltung 

    • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
    • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
    • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

     

    Lernziele
    Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

    Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

    • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
    • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
    • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
    • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
    • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

     

    Formalia & Organisatorisches
    a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
    b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

    • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
    • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
    • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

    c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
     

  • 20110401 Lecture
    Quantum information theory (Jens Eisert)
    Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
    Location: Di 0.1.01 Hörsaal B (Arnimallee 14), Do 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Information theory usually abstracts from the underlying physical carriers of information: There is no "hard-drive information" any different from "newspaper information". This is because one type of information can be transformed into another one in a lossless fashion, and hence the actual physical carrier does not matter when it comes to thinking about what ways of processing of information are possible. Things change dramatically, however, if single quantum systems - such as trapped ions, cold atoms, or light quanta - are taken as elementary carriers of information. This course will give an introduction into what is possible pursuing this idea. We will discuss applications of quantum key distribution (allowing for the secure transmission of information), quantum computing (giving rise to computers that can solve some problems faster than conventional supercomputers), quantum simulation (allowing to simulate other complex quantum systems) and sensing devices. For this, we will develop the underlying quantum information theory, with notions of entanglement taking center stage. These applications are subsumed into what is now often called quantum technologies. Specific emphasis will finally be put onto elaborating on the intersection of quantum information theory on the one hand and condensed-matter physics on the other, where new perspectives arise.

  • 19205402 Practice seminar
    Exercise for Basic Module: Topology I (Sofia Garzón Mora)
    Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    
  • 19214502 Practice seminar
    Practice seminar for Basic Module: Algebra II (Georg Lehner)
    Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19214702 Practice seminar
    Practice seminar for Discrete Mathematics I (Silas Rathke)
    Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Comments

    Content:

    Selection from the following topics:

    • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)
    • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)

  • 19214902 Practice seminar
    Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19215202 Practice seminar
    Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
    Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Homepage:Wiki der Numerik II

  • 19215602 Practice seminar Cancelled
    Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Am 23. April findet keine Übung statt.

  • 19241302 Practice seminar
    Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
    Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    
  • 19248102 Practice seminar
    Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    
  • 20110402 Practice seminar
    Quantum information theory (Jens Eisert)
    Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: Mo 1.1.53 Seminarraum E2 (Arnimallee 14), Mo 1.3.48 Seminarraum T3 (Arnimallee 14), Mo 1.4.31 Seminarraum E3 (Arnimallee 14), Di 1.1.16 FB-Raum (Arnimallee 14)
    

• Complementary Module: Specific Research Aspects

  0280cA4.10
  • 19219701 Lecture
    Algebra with Probability in Combinatorics (Tibor Szabo)
    Schedule: Do 08:00-10:00 (Class starts on: 2025-04-17)
    Location: T9/049 Seminarraum (Takustr. 9)
    

    Comments

    In this lecture specialized topics of Combinatorics and Graph Theory are presented.

• Complementary Module: BMS – Fridays

  0280cA4.12
  • 19223111 Seminar
    BMS Fridays (Holger Reich)
    Schedule: Fr 14:00-17:00 (Class starts on: 2025-04-25)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

    The Friday colloquia of BMS represent a common meeting point for Berlin mathematics at Urania Berlin: a colloquium with broad emanation that permits an overview of large-scale connections and insights. In thematic series, the conversation is about “mathematics as a whole,” and we hope to be able to witness some breakthroughs.

    Typically, there is a BMS colloquium every other Friday afternoon in the BMS Loft at Urania during term time. BMS Friday colloquia usually start at 2:15 pm. Tea and cookies are served before each talk at 1:00 pm.

    More details: https://www.math-berlin.de/academics/bms-fridays

• Complementary Module: What is …?

  0280cA4.13
  • 19217311 Seminar
    PhD Seminar "What is...?" (Holger Reich)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-18)
    Location: A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    The "What is ...?" seminars are usually held before the BMS Friday seminar to complement the topic of the talk.

    Audience: Anybody interested in mathematics is invited to attend the "What is ...?" seminars. This includes Bachelors, Masters, Diplom, and PhD students from any field, as well as researchers like Post-Docs.
    Requirements: The speakers assume that the audience has at least a general knowledge of graduate-level mathematics.

    Comments

    Content: The "What is ...?" seminar is a 30-minute weekly seminar that concisely introduces terms and ideas that are fundamental to certain fields of mathematics but may not be familiar in others.
    The vast mathematical landscape in Berlin welcomes mathematicians with diverse backgrounds to work side by side, yet their paths often only cross within their individual research groups. To encourage interdisciplinary cooperation and collaboration, the "What is ...?" seminar attempts to initiate contact by introducing essential vocabulary and foundational concepts of the numerous fields represented in Berlin. The casual atmosphere of the seminar invites the audience to ask many questions and the speakers to experiment with their presentation styles.
    The location of the seminar rotates among the Urania, FU, TU, and HU. On the weeks when a BMS Friday takes place, the "What is ...?" seminar topic is arranged to coincide with the Friday talk acting as an introductory talk for the BMS Friday Colloquium. For a schedule of the talks and their locations, check the website. The website is updated frequently throughout the semester.

    Talks and more detailed information can be found here
    Homepage: http://www.math.fu-berlin.de/w/Math/WhatIsSeminar

• Complementary Module: Selected Topics B

  0280cA4.2
  • 19205401 Lecture
    Basic module: Topology I (Christian Haase)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    
    Course Overview This is a beginning course from the series of three courses Topology I—III:

    1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
    2. Groups acting on topological spaces
    3. Gluing constructions, simplicial complexes
    4. Homotopies between continuous maps, degree of a map, fundamental group.
    5. Seifert-van Kampen Theorem.
    6. Covering spaces.
    7. Simplicial homology
    8. Combinatorial applications

    Suggested reading

    Literature:

    1. M. A. Armstron: Basic Topology, Springer UTM
    2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
    3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
    4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
    5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
    6. Klaus Jänich: Topologie, Springer-Verlag
    7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
    8. James R. Munkres: Topology, Prentice Hall

  • 19214501 Lecture
    Basic Module: Algebra II (Holger Reich)
    Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisits: Comutitive algebra

    Comments

    The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

    Possible topics include: 
    - categories and functors
    - additive and abelian categories
    - cohomology
    - sheaf theory
    - ringed spaces
    - schemes
    - separated and proper morphisms
    - blowing up
    - embeddings into projective spaces, divisors, invertible sheaves 
    - Riemann-Roch -Gröbner bases.

    Suggested reading

    For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten

  • 19214701 Lecture
    Discrete Mathematics I (Ralf Borndörfer)
    Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Target group:

    BMS students, Master and Bachelor students

    Whiteboard:

    You need access to the whiteboard in order to receive information and participate in the exercises.

    Large tutorial:

    Participation is recommended, but non-mandatory.

    Exams:

    1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
    2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

    Comments

    Content:

    Selection from the following topics:

    • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)

    Suggested reading

    • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
    • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
    • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
    • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
    • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.

  • 19214901 Lecture
    Basic Module: Discrete Geometrie II (Georg Loho)
    Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

    Comments

    Inhalt:

    This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

    The material will be a selection of the following topics:
    Linear programming and some applications

     

    • Linear programming and duality
    • Pivot rules and the diameter of polytopes

    Subdivisions and triangulations

    • Delaunay and Voronoi
    • Delaunay triangulations and inscribable polytopes
    • Weighted Voronoi diagrams and optimal transport

    Basic structures in convex geometry

     

    • convexity and separation theorems
    • convex bodies and polytopes/polyhedra
    • polarity
    • Mahler’s conjecture
    • approximation by polytopes

    Volumes and roundness

    • Hilbert’s third problem
    • volumes and mixed volumes
    • volume computations and estimates
    • Löwner-John ellipsoids and roundness
    • valuations

    Geometric inequalities

    • Brunn-Minkowski and Alexandrov-Fenchel inequality
    • isoperimetric inequalities
    • measure concentration and phenomena in high-dimensions

    Geometry of numbers

    • lattices
    • Minkowski's (first) theorem
    • successive minima
    • lattice points in convex bodies and Ehrhart's theorem
    • Ehrhart-Macdonald reciprocity

    Sphere packings

    • lattice packings and coverings
    • the Theorem of Minkowski-Hlawka
    • analytic methods

    Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

    Suggested reading

    The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.

  • 19215201 Lecture
    Basic Module: Numerics III (Volker John)
    Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisites

    Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

    Comments

    The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

     

    Suggested reading

    • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
    • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)

  • 19215601 Lecture Cancelled
    Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

    Comments

    Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

    Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

    Suggested reading

    L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

    Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).

  • 19241301 Lecture
    Partial Differential Equations I (André Erhardt)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Comments

    • Basic differential equations (Laplace,- heat and wave equations)
    • Representation formulas
    • Solution methods
    • Introduction to Hilbert space methods

    This can serve as the basis for a BSc and/or MSc project.  

    Suggested reading

    L.C. Evans, Partial Differential Equations
     

  • 19248101 Lecture
    Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
     

    Leitidee der Veranstaltung
    Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

    Inhaltliche Schwerpunkte
    Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

    Methodische Konzeption
    Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

    Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
    Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

    Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
     

    Überblick über die wöchentliche Struktur der Veranstaltung 

    • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
    • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
    • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

     

    Lernziele
    Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

    Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

    • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
    • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
    • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
    • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
    • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

     

    Formalia & Organisatorisches
    a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
    b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

    • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
    • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
    • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

    c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
     

  • 20110401 Lecture
    Quantum information theory (Jens Eisert)
    Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
    Location: Di 0.1.01 Hörsaal B (Arnimallee 14), Do 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Information theory usually abstracts from the underlying physical carriers of information: There is no "hard-drive information" any different from "newspaper information". This is because one type of information can be transformed into another one in a lossless fashion, and hence the actual physical carrier does not matter when it comes to thinking about what ways of processing of information are possible. Things change dramatically, however, if single quantum systems - such as trapped ions, cold atoms, or light quanta - are taken as elementary carriers of information. This course will give an introduction into what is possible pursuing this idea. We will discuss applications of quantum key distribution (allowing for the secure transmission of information), quantum computing (giving rise to computers that can solve some problems faster than conventional supercomputers), quantum simulation (allowing to simulate other complex quantum systems) and sensing devices. For this, we will develop the underlying quantum information theory, with notions of entanglement taking center stage. These applications are subsumed into what is now often called quantum technologies. Specific emphasis will finally be put onto elaborating on the intersection of quantum information theory on the one hand and condensed-matter physics on the other, where new perspectives arise.

  • 19205402 Practice seminar
    Exercise for Basic Module: Topology I (Sofia Garzón Mora)
    Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    
  • 19214502 Practice seminar
    Practice seminar for Basic Module: Algebra II (Georg Lehner)
    Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19214702 Practice seminar
    Practice seminar for Discrete Mathematics I (Silas Rathke)
    Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Comments

    Content:

    Selection from the following topics:

    • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)
    • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)

  • 19214902 Practice seminar
    Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19215202 Practice seminar
    Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
    Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Homepage:Wiki der Numerik II

  • 19215602 Practice seminar Cancelled
    Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Am 23. April findet keine Übung statt.

  • 19241302 Practice seminar
    Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
    Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    
  • 19248102 Practice seminar
    Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    
  • 20110402 Practice seminar
    Quantum information theory (Jens Eisert)
    Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: Mo 1.1.53 Seminarraum E2 (Arnimallee 14), Mo 1.3.48 Seminarraum T3 (Arnimallee 14), Mo 1.4.31 Seminarraum E3 (Arnimallee 14), Di 1.1.16 FB-Raum (Arnimallee 14)
    

• Complementary Module: Selected Topics C

  0280cA4.3
  • 19205401 Lecture
    Basic module: Topology I (Christian Haase)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    
    Course Overview This is a beginning course from the series of three courses Topology I—III:

    1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
    2. Groups acting on topological spaces
    3. Gluing constructions, simplicial complexes
    4. Homotopies between continuous maps, degree of a map, fundamental group.
    5. Seifert-van Kampen Theorem.
    6. Covering spaces.
    7. Simplicial homology
    8. Combinatorial applications

    Suggested reading

    Literature:

    1. M. A. Armstron: Basic Topology, Springer UTM
    2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
    3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
    4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
    5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
    6. Klaus Jänich: Topologie, Springer-Verlag
    7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
    8. James R. Munkres: Topology, Prentice Hall

  • 19214501 Lecture
    Basic Module: Algebra II (Holger Reich)
    Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisits: Comutitive algebra

    Comments

    The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

    Possible topics include: 
    - categories and functors
    - additive and abelian categories
    - cohomology
    - sheaf theory
    - ringed spaces
    - schemes
    - separated and proper morphisms
    - blowing up
    - embeddings into projective spaces, divisors, invertible sheaves 
    - Riemann-Roch -Gröbner bases.

    Suggested reading

    For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten

  • 19214701 Lecture
    Discrete Mathematics I (Ralf Borndörfer)
    Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Target group:

    BMS students, Master and Bachelor students

    Whiteboard:

    You need access to the whiteboard in order to receive information and participate in the exercises.

    Large tutorial:

    Participation is recommended, but non-mandatory.

    Exams:

    1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
    2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

    Comments

    Content:

    Selection from the following topics:

    • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)

    Suggested reading

    • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
    • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
    • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
    • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
    • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.

  • 19214901 Lecture
    Basic Module: Discrete Geometrie II (Georg Loho)
    Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

    Comments

    Inhalt:

    This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

    The material will be a selection of the following topics:
    Linear programming and some applications

     

    • Linear programming and duality
    • Pivot rules and the diameter of polytopes

    Subdivisions and triangulations

    • Delaunay and Voronoi
    • Delaunay triangulations and inscribable polytopes
    • Weighted Voronoi diagrams and optimal transport

    Basic structures in convex geometry

     

    • convexity and separation theorems
    • convex bodies and polytopes/polyhedra
    • polarity
    • Mahler’s conjecture
    • approximation by polytopes

    Volumes and roundness

    • Hilbert’s third problem
    • volumes and mixed volumes
    • volume computations and estimates
    • Löwner-John ellipsoids and roundness
    • valuations

    Geometric inequalities

    • Brunn-Minkowski and Alexandrov-Fenchel inequality
    • isoperimetric inequalities
    • measure concentration and phenomena in high-dimensions

    Geometry of numbers

    • lattices
    • Minkowski's (first) theorem
    • successive minima
    • lattice points in convex bodies and Ehrhart's theorem
    • Ehrhart-Macdonald reciprocity

    Sphere packings

    • lattice packings and coverings
    • the Theorem of Minkowski-Hlawka
    • analytic methods

    Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

    Suggested reading

    The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.

  • 19215201 Lecture
    Basic Module: Numerics III (Volker John)
    Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisites

    Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

    Comments

    The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

     

    Suggested reading

    • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
    • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)

  • 19215601 Lecture Cancelled
    Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

    Comments

    Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

    Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

    Suggested reading

    L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

    Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).

  • 19241301 Lecture
    Partial Differential Equations I (André Erhardt)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Comments

    • Basic differential equations (Laplace,- heat and wave equations)
    • Representation formulas
    • Solution methods
    • Introduction to Hilbert space methods

    This can serve as the basis for a BSc and/or MSc project.  

    Suggested reading

    L.C. Evans, Partial Differential Equations
     

  • 19248101 Lecture
    Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
     

    Leitidee der Veranstaltung
    Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

    Inhaltliche Schwerpunkte
    Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

    Methodische Konzeption
    Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

    Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
    Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

    Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
     

    Überblick über die wöchentliche Struktur der Veranstaltung 

    • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
    • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
    • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

     

    Lernziele
    Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

    Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

    • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
    • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
    • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
    • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
    • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

     

    Formalia & Organisatorisches
    a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
    b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

    • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
    • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
    • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

    c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
     

  • 20110401 Lecture
    Quantum information theory (Jens Eisert)
    Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
    Location: Di 0.1.01 Hörsaal B (Arnimallee 14), Do 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Information theory usually abstracts from the underlying physical carriers of information: There is no "hard-drive information" any different from "newspaper information". This is because one type of information can be transformed into another one in a lossless fashion, and hence the actual physical carrier does not matter when it comes to thinking about what ways of processing of information are possible. Things change dramatically, however, if single quantum systems - such as trapped ions, cold atoms, or light quanta - are taken as elementary carriers of information. This course will give an introduction into what is possible pursuing this idea. We will discuss applications of quantum key distribution (allowing for the secure transmission of information), quantum computing (giving rise to computers that can solve some problems faster than conventional supercomputers), quantum simulation (allowing to simulate other complex quantum systems) and sensing devices. For this, we will develop the underlying quantum information theory, with notions of entanglement taking center stage. These applications are subsumed into what is now often called quantum technologies. Specific emphasis will finally be put onto elaborating on the intersection of quantum information theory on the one hand and condensed-matter physics on the other, where new perspectives arise.

  • 19205402 Practice seminar
    Exercise for Basic Module: Topology I (Sofia Garzón Mora)
    Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    
  • 19214502 Practice seminar
    Practice seminar for Basic Module: Algebra II (Georg Lehner)
    Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19214702 Practice seminar
    Practice seminar for Discrete Mathematics I (Silas Rathke)
    Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Comments

    Content:

    Selection from the following topics:

    • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)
    • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)

  • 19214902 Practice seminar
    Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19215202 Practice seminar
    Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
    Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Homepage:Wiki der Numerik II

  • 19215602 Practice seminar Cancelled
    Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Am 23. April findet keine Übung statt.

  • 19241302 Practice seminar
    Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
    Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    
  • 19248102 Practice seminar
    Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    
  • 20110402 Practice seminar
    Quantum information theory (Jens Eisert)
    Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: Mo 1.1.53 Seminarraum E2 (Arnimallee 14), Mo 1.3.48 Seminarraum T3 (Arnimallee 14), Mo 1.4.31 Seminarraum E3 (Arnimallee 14), Di 1.1.16 FB-Raum (Arnimallee 14)
    

• Complementary Module: Specific Aspects A

  0280cA4.4
  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

    Requirements: basic courses in analysis, basic course numerical mathematics

    Literature:

    Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
    https://doi.org/10.3390/atmos14101523

    T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

    J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

    Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000

  • 19215001 Lecture
    Constructive Combinatorics (Tibor Szabo)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Basic Bachelor Algebra, Probability, and Disrete Mathematics.

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

    Suggested reading

    A script will be provided.

  • 19215301 Lecture
    Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Content:

    Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

    Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

     

    This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

    The course will cover a selection from the following topics

    1. Conservation laws and governing equations,

    2. Numerical methods for geophysical flow simulations,

    3. Dynamical systems and bifurcation theory,

    4. Data-based characterization of atmospheric flows

     

    This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

    Suggested reading

    Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

    Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

     

  • 19222601 Lecture
    Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Zielgruppe: Students who are interested in stochastics and numerics
    Voraussetzungen: Stochastik I + II, Numerik I + II

    Comments

    Inhalt der Veranstaltung:
    The lecture will cover the following topics (not exhaustive)

    • Brownian motion 
    • Numerical discretization of stochastic differential equations
    • Monte Carlo methods
    • Representations of random fields
    • Modelling with stochastic differential equations
    • Applications

    Suggested reading

    Literatur:

    1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
    2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
    3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
    4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
    5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014

  • 19223901 Lecture
    Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
    Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

    Suggested reading

    The following books will be relevant:

    • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
    • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
    • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
    • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.

  • 19229601 Lecture Cancelled
    Stochastic dynamics in fluids (Felix Höfling)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Target audience: M.Sc. Computational Sciences/Mathematik/Physik

    Requirements: some advanced course on either statistical physics or stochastic processes

    Comments

    The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

    The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

    Keywords:

    • Brownian motion, diffusion, and stochastic processes in fluids
    • harmonic analysis of correlation functions
    • Zwanzig-Mori projection operator formalism
    • mode-coupling approximations, long-time tails
    • critical dynamics and transport anomalies

    Suggested reading

    • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
    • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

    Further literature will be given during the course.

  • 19234501 Lecture
    Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: T9/053 Seminarraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of stochastics, and numerical methods

    Comments

    Content:

    Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

    - Basic of stochastic processes:

    Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

    - Model reduction techniques for stochastic dynamics:

    averaging technique, effective dynamics, Markov state modeling

    - Machine learning techniques using/for stochastic dynamics: 

    dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

    Suggested reading

    1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

    2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

    3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

    4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

    5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

    6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.

  • 19240701 Lecture
    Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

    Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

    Comments

    Prpgram:

    -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

  • 19242101 Lecture
    Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I, II, III. 
    Recommended: Functional Analysis.

    Comments

    Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

    • Ito calculus for Gaussian random measures;
    • semilinear stochastic PDEs in one dimension;
    • Schauder estimates;
    • Gaussian hypercontractivity;
    • paraproducts and paracontrolled distributions;
    • local existence and uniqueness for semilinear SPDEs in higher dimensions;
    • properties of solutions

    Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

    Suggested reading

    Literature
    There will be lecture notes.

  • 19243001 Lecture
    Partial Differential Equations III (Erica Ipocoana)
    Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Voraussetzungen: Partielle Differentialgleichungen I und II

    Comments

    The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

     

    Suggested reading

    Wird in der Vorlesung bekannt gegeben / to be announced.

  • 19207102 Practice seminar
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19215002 Practice seminar
    Constructive Combinatorics exercises (Tibor Szabo)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

  • 19215302 Practice seminar
    Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    
  • 19222602 Practice seminar
    Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19223902 Practice seminar
    Übung zu UQ and QMC (Claudia Schillings)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19229602 Practice seminar Cancelled
    Exercises to Stochastic processes in fluids (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19234502 Practice seminar
    Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

  • 19240702 Practice seminar
    Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    
  • 19242102 Practice seminar
    Exercise: Stochastics IV (Guilherme de Lima Feltes)
    Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19243002 Practice seminar
    Tutorial Partial Differential Equations III (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
    Location: A3/SR 119 (Arnimallee 3-5)
    

• Complementary Module: Specific Aspects B

  0280cA4.5
  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

    Requirements: basic courses in analysis, basic course numerical mathematics

    Literature:

    Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
    https://doi.org/10.3390/atmos14101523

    T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

    J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

    Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000

  • 19215001 Lecture
    Constructive Combinatorics (Tibor Szabo)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Basic Bachelor Algebra, Probability, and Disrete Mathematics.

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

    Suggested reading

    A script will be provided.

  • 19215301 Lecture
    Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Content:

    Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

    Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

     

    This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

    The course will cover a selection from the following topics

    1. Conservation laws and governing equations,

    2. Numerical methods for geophysical flow simulations,

    3. Dynamical systems and bifurcation theory,

    4. Data-based characterization of atmospheric flows

     

    This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

    Suggested reading

    Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

    Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

     

  • 19222601 Lecture
    Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Zielgruppe: Students who are interested in stochastics and numerics
    Voraussetzungen: Stochastik I + II, Numerik I + II

    Comments

    Inhalt der Veranstaltung:
    The lecture will cover the following topics (not exhaustive)

    • Brownian motion 
    • Numerical discretization of stochastic differential equations
    • Monte Carlo methods
    • Representations of random fields
    • Modelling with stochastic differential equations
    • Applications

    Suggested reading

    Literatur:

    1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
    2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
    3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
    4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
    5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014

  • 19223901 Lecture
    Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
    Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

    Suggested reading

    The following books will be relevant:

    • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
    • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
    • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
    • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.

  • 19229601 Lecture Cancelled
    Stochastic dynamics in fluids (Felix Höfling)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Target audience: M.Sc. Computational Sciences/Mathematik/Physik

    Requirements: some advanced course on either statistical physics or stochastic processes

    Comments

    The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

    The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

    Keywords:

    • Brownian motion, diffusion, and stochastic processes in fluids
    • harmonic analysis of correlation functions
    • Zwanzig-Mori projection operator formalism
    • mode-coupling approximations, long-time tails
    • critical dynamics and transport anomalies

    Suggested reading

    • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
    • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

    Further literature will be given during the course.

  • 19234501 Lecture
    Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: T9/053 Seminarraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of stochastics, and numerical methods

    Comments

    Content:

    Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

    - Basic of stochastic processes:

    Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

    - Model reduction techniques for stochastic dynamics:

    averaging technique, effective dynamics, Markov state modeling

    - Machine learning techniques using/for stochastic dynamics: 

    dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

    Suggested reading

    1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

    2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

    3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

    4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

    5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

    6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.

  • 19240701 Lecture
    Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

    Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

    Comments

    Prpgram:

    -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

  • 19242101 Lecture
    Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I, II, III. 
    Recommended: Functional Analysis.

    Comments

    Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

    • Ito calculus for Gaussian random measures;
    • semilinear stochastic PDEs in one dimension;
    • Schauder estimates;
    • Gaussian hypercontractivity;
    • paraproducts and paracontrolled distributions;
    • local existence and uniqueness for semilinear SPDEs in higher dimensions;
    • properties of solutions

    Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

    Suggested reading

    Literature
    There will be lecture notes.

  • 19243001 Lecture
    Partial Differential Equations III (Erica Ipocoana)
    Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Voraussetzungen: Partielle Differentialgleichungen I und II

    Comments

    The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

     

    Suggested reading

    Wird in der Vorlesung bekannt gegeben / to be announced.

  • 19207102 Practice seminar
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19215002 Practice seminar
    Constructive Combinatorics exercises (Tibor Szabo)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

  • 19215302 Practice seminar
    Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    
  • 19222602 Practice seminar
    Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19223902 Practice seminar
    Übung zu UQ and QMC (Claudia Schillings)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19229602 Practice seminar Cancelled
    Exercises to Stochastic processes in fluids (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19234502 Practice seminar
    Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

  • 19240702 Practice seminar
    Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    
  • 19242102 Practice seminar
    Exercise: Stochastics IV (Guilherme de Lima Feltes)
    Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19243002 Practice seminar
    Tutorial Partial Differential Equations III (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
    Location: A3/SR 119 (Arnimallee 3-5)
    

• Complementary Module: Specific Aspects C

  0280cA4.6
  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

    Requirements: basic courses in analysis, basic course numerical mathematics

    Literature:

    Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
    https://doi.org/10.3390/atmos14101523

    T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

    J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

    Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000

  • 19215001 Lecture
    Constructive Combinatorics (Tibor Szabo)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Basic Bachelor Algebra, Probability, and Disrete Mathematics.

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

    Suggested reading

    A script will be provided.

  • 19215301 Lecture
    Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Content:

    Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

    Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

     

    This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

    The course will cover a selection from the following topics

    1. Conservation laws and governing equations,

    2. Numerical methods for geophysical flow simulations,

    3. Dynamical systems and bifurcation theory,

    4. Data-based characterization of atmospheric flows

     

    This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

    Suggested reading

    Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

    Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

     

  • 19222601 Lecture
    Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Zielgruppe: Students who are interested in stochastics and numerics
    Voraussetzungen: Stochastik I + II, Numerik I + II

    Comments

    Inhalt der Veranstaltung:
    The lecture will cover the following topics (not exhaustive)

    • Brownian motion 
    • Numerical discretization of stochastic differential equations
    • Monte Carlo methods
    • Representations of random fields
    • Modelling with stochastic differential equations
    • Applications

    Suggested reading

    Literatur:

    1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
    2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
    3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
    4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
    5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014

  • 19223901 Lecture
    Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
    Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

    Suggested reading

    The following books will be relevant:

    • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
    • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
    • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
    • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.

  • 19229601 Lecture Cancelled
    Stochastic dynamics in fluids (Felix Höfling)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Target audience: M.Sc. Computational Sciences/Mathematik/Physik

    Requirements: some advanced course on either statistical physics or stochastic processes

    Comments

    The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

    The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

    Keywords:

    • Brownian motion, diffusion, and stochastic processes in fluids
    • harmonic analysis of correlation functions
    • Zwanzig-Mori projection operator formalism
    • mode-coupling approximations, long-time tails
    • critical dynamics and transport anomalies

    Suggested reading

    • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
    • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

    Further literature will be given during the course.

  • 19234501 Lecture
    Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: T9/053 Seminarraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of stochastics, and numerical methods

    Comments

    Content:

    Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

    - Basic of stochastic processes:

    Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

    - Model reduction techniques for stochastic dynamics:

    averaging technique, effective dynamics, Markov state modeling

    - Machine learning techniques using/for stochastic dynamics: 

    dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

    Suggested reading

    1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

    2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

    3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

    4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

    5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

    6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.

  • 19240701 Lecture
    Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

    Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

    Comments

    Prpgram:

    -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

  • 19242101 Lecture
    Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I, II, III. 
    Recommended: Functional Analysis.

    Comments

    Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

    • Ito calculus for Gaussian random measures;
    • semilinear stochastic PDEs in one dimension;
    • Schauder estimates;
    • Gaussian hypercontractivity;
    • paraproducts and paracontrolled distributions;
    • local existence and uniqueness for semilinear SPDEs in higher dimensions;
    • properties of solutions

    Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

    Suggested reading

    Literature
    There will be lecture notes.

  • 19243001 Lecture
    Partial Differential Equations III (Erica Ipocoana)
    Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Voraussetzungen: Partielle Differentialgleichungen I und II

    Comments

    The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

     

    Suggested reading

    Wird in der Vorlesung bekannt gegeben / to be announced.

  • 19207102 Practice seminar
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19215002 Practice seminar
    Constructive Combinatorics exercises (Tibor Szabo)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

  • 19215302 Practice seminar
    Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    
  • 19222602 Practice seminar
    Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19223902 Practice seminar
    Übung zu UQ and QMC (Claudia Schillings)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19229602 Practice seminar Cancelled
    Exercises to Stochastic processes in fluids (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19234502 Practice seminar
    Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

  • 19240702 Practice seminar
    Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    
  • 19242102 Practice seminar
    Exercise: Stochastics IV (Guilherme de Lima Feltes)
    Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19243002 Practice seminar
    Tutorial Partial Differential Equations III (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
    Location: A3/SR 119 (Arnimallee 3-5)
    

• Complementary Module: Current Research Topics A

  0280cA4.7
  • 19206011 Seminar
    Discrete Mathematics Masterseminar (Tibor Szabo)
    Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

     

     

    Comments

    Content:
    The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
    Target audience:
    BMS students, Master students, or advanced Bachelor students.
    Prerequisites:
    Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

     

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Comments

    Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

    The discussion will concerns both, specific computational coding and conceptual developments.

    Suggested reading

    Related Basic Literature:

    (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

    (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

    (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science

  • 19226611 Seminar
    Seminar Quantum Computational Methods (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

    Comments

    The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
    In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
    Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

    Suggested reading

    Related Basic Literature:
    (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
    (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
    (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871

  • 19227611 Seminar
    Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Comments

    The seminar covers advanced topics of uncertainty quantification and inverse problems.

  • 19239711 Seminar
    Advanced Dynamical Systems (Bernold Fiedler)
    Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in delay equations. Dates only by arrangement.

  • 19239911 Seminar
    Advanced Differential Equations (Bernold Fiedler)
    Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in dynamical systems. Dates only by arrangement.

  • 19247111 Seminar
    Variational methods & Gamma-convergence (Marita Thomas)
    Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

• Complementary Module: Current Research Topics B

  0280cA4.8
  • 19206011 Seminar
    Discrete Mathematics Masterseminar (Tibor Szabo)
    Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

     

     

    Comments

    Content:
    The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
    Target audience:
    BMS students, Master students, or advanced Bachelor students.
    Prerequisites:
    Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

     

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Comments

    Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

    The discussion will concerns both, specific computational coding and conceptual developments.

    Suggested reading

    Related Basic Literature:

    (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

    (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

    (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science

  • 19226611 Seminar
    Seminar Quantum Computational Methods (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

    Comments

    The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
    In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
    Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

    Suggested reading

    Related Basic Literature:
    (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
    (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
    (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871

  • 19227611 Seminar
    Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Comments

    The seminar covers advanced topics of uncertainty quantification and inverse problems.

  • 19239711 Seminar
    Advanced Dynamical Systems (Bernold Fiedler)
    Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in delay equations. Dates only by arrangement.

  • 19239911 Seminar
    Advanced Differential Equations (Bernold Fiedler)
    Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in dynamical systems. Dates only by arrangement.

  • 19247111 Seminar
    Variational methods & Gamma-convergence (Marita Thomas)
    Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

• Complementary Module: Current Research Topics C

  0280cA4.9
  • 19206011 Seminar
    Discrete Mathematics Masterseminar (Tibor Szabo)
    Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

     

     

    Comments

    Content:
    The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
    Target audience:
    BMS students, Master students, or advanced Bachelor students.
    Prerequisites:
    Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

     

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Comments

    Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

    The discussion will concerns both, specific computational coding and conceptual developments.

    Suggested reading

    Related Basic Literature:

    (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

    (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

    (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science

  • 19226611 Seminar
    Seminar Quantum Computational Methods (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

    Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

    Comments

    The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
    In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
    Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

    Suggested reading

    Related Basic Literature:
    (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
    (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
    (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871

  • 19227611 Seminar
    Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Comments

    The seminar covers advanced topics of uncertainty quantification and inverse problems.

  • 19239711 Seminar
    Advanced Dynamical Systems (Bernold Fiedler)
    Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in delay equations. Dates only by arrangement.

  • 19239911 Seminar
    Advanced Differential Equations (Bernold Fiedler)
    Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in dynamical systems. Dates only by arrangement.

  • 19247111 Seminar
    Variational methods & Gamma-convergence (Marita Thomas)
    Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

• Modules w/o courses in this semester

  25 Modules
  • Introductory Module: Algebra I 0280cA1.1
  • Introductory Module: Dynamical Systems II 0280cA1.10
  • Introductory Module: Numerical Mathematics II 0280cA1.11
  • Introductory Module: Partial Differential Equations II 0280cA1.14
  • Introductory Module: Probability and Statistics II 0280cA1.15
  • Introductory Module: Probability and Statistics III 0280cA1.16
  • Introductory Module: Topology II 0280cA1.18
  • Introductory Module: Number Theory II 0280cA1.19
  • Introductory Module: Differential Geometry I 0280cA1.3
  • Introductory Module: Differential Geometry II 0280cA1.4
  • Introductory Module: Discrete Geometry I 0280cA1.5
  • Introductory Module: Discrete Mathematics II 0280cA1.8
  • Advanced Module: Algebra III 0280cA2.1
  • Advanced Module: Number Theory III 0280cA2.10
  • Advanced Module: Differential Geometry III 0280cA2.2
  • Advanced Module: Discrete Geometry III 0280cA2.3
  • Advanced Module: Dynamical Systems III 0280cA2.5
  • Advanced Module: Topology III 0280cA2.9
  • Specialization Module: Master's Seminar on Algebra 0280cA3.1
  • Specialization Module: Master's Seminar on Number Theory 0280cA3.10
  • Specialization Module: Master's Seminar on Differential Geometry 0280cA3.2
  • Specialization Module: Master's Seminar on Discrete Geometry 0280cA3.3
  • Specialization Module: Master’s Seminar on Dynamical Systems 0280cA3.5
  • Specialization Module: Master’s Seminar on Probability and Statistics 0280cA3.8
  • Complementary Module: Research Project 0280cA4.11