Computer Science

• Analysis II

  0084dA1.2
  • 19211601 Lecture
    Analysis II (Pavle Blagojevic)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Content

    1. Additions to Analysis I. Non-authentic integrals
    2. Uniform convergence of function sequences. Power series. Sentence of Taylor.
    3. Elements of topology. Standardized and metric spaces. Open quantities. Convergence. Completed quantities. Consistency. Compactness
    4. Differential calculus of several variables. Partial, total and continuous differentiability. Block via the inverse function. Block of implicit functions.
    5. Iterated integrals.
    6. Ordinary differential equations. Basic terms, elementary solvable differential equations, existential and unambiguous results for systems.

    Suggested reading

    • O. Forster: Analysis 1 und 2. Vieweg/Springer.
    • Königsberger, K: Analysis 1,2, Springer.
    • E. Behrends: Analysis Band 1 und 2, Vieweg/Springer.
    • H. Heuser: Lehrbuch der Analysis 1 und 2, Teubner/Springer.

• Analysis III

  0084dA1.3
  • 19201301 Lecture
    Analysis III (Marita Thomas)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Contents

    The lecture Analysis III is the final lecture of the cycle Analysis I-III.

    • ODEs
    • ^{Differentiation and integration in Rn},
    • extremes with and without constraints,
    • integration on surfaces,
    • the integrals of Gauss and Stokes and much more are discussed.

    These basics are indispensable for a successful study of mathematics.

    Suggested reading

    Literatur

    • H. Amann, J. Escher: Analysis 2, Birkhäuser Verlag, 2008.
    • H. Amann, J. Escher: Analysis 3, Birkhäuser Verlag, 2008.
    • O. Forster: Analysis 2, Springer Verlag, 2012.
    • O. Forster: Analysis 3, Vieweg+Teubner, 2012.
    • H. Heuser: Lehrbuch der Analysis 2, Vieweg+Teubner, 2012.
    • S. Hildebrandt: Analysis 2, Springer Verlag, 2003.
    • J. Jost: Postmodern Analysis, Springer Verlag, 2008.
    • K. Königsberger: Analysis 2, Springer Verlag, 2004.
    • W. Rudin: Principles of Mathematical Analysis, International Series in Pure & Applied Mathematics, 1976.

    und für geschichtlich Interessierte:

    • O. Becker: Grundlagen der Mathematik, Verlag Karl Alber, Freiburg, 1964.
    • E. Hairer, G. Wanner: Analysis by its History, Springer, 2000.
    • V.J. Katz: A History of Mathematics, Harper Collins, New York, 1993.

  • 19201302 Practice seminar
    Practice seminar for Analysis III (Marita Thomas, Sven Tornquist)
    Schedule: Di 14:00-16:00, Mi 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

• Linear Algebra II

  0084dA1.5
  • 19211702 Practice seminar
    Practice seminar for Linear Algebra II (Marcus Weber)
    Schedule: Di 08:00-10:00, Di 14:00-16:00, Mi 12:00-14:00, Do 16:00-18:00, Fr 08:00-10:00 (Class starts on: 2025-10-14)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

• Computer-Oriented Mathematics I

  0084dA1.6
  • 19200501 Lecture
    Computerorientated Mathematics I (5 LP) (Claudia Schillings)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

    Contents:
    Computers play an important role in (almost) all situations in life today. Computer-oriented mathematics provides basic knowledge in dealing with computers for solving mathematical problems and an introduction to algorithmic thinking. At the same time, typical mathematical software such as Matlab and Mathematica will be introduced. The motivation for the questions under consideration is provided by simple application examples from the aforementioned areas. The content of the first part includes fundamental terms of numerical calculation: number representation and rounding errors, condition, efficiency and stability.

    Homepage: All current information on lectures and lectures

    Suggested reading

    Literatur: R. Kornhuber, C. Schuette, A. Fest: Mit Zahlen Rechnen (Skript zur Vorlesung)

  • 19200502 Practice seminar
    Practice seminar for Computerorientated Mathematics I (5 LP) (N.N.)
    Schedule: Mo 12:00-14:00, Mo 14:00-16:00, Di 08:00-10:00, Di 16:00-18:00, Mi 10:00-12:00, Do 14:00-16:00, Fr 08:00-10:00 (Class starts on: 2025-10-13)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Numerical Mathematics I

  0084dA1.9
  • 19212001 Lecture
    Numerics I (Volker John)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-13)
    Location: A7/SR 031 (Arnimallee 7)
    

    Comments

    Numerical methods for: iterative solution of nonlinear systems of equations (fixpoint and Newton methods), curve fitting, interpolation, numerical quadrature, and numerics for initial value problems and two point boundary value problems with ODEs. The course is taught in German.

    Suggested reading

    Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 1. Springer, Berlin, 2005.

    Aus dem FU-Netz auch online verfügbar.

    Es wird ein Vorlesungsskript geben.

    Link

  • 19212002 Practice seminar
    Practice seminar for Numerics I (N.N.)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A7/SR 031 (Arnimallee 7)
    

• Academic Work in Mathematics

  0084dB1.1
  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
    Location: SR A9
    

    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

  • 19240317 Seminar / Undergraduate Course
    Advancing mathematics with AI (Georg Loho)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    The course will probably be held in German. 

  • 19247111 Seminar
    Ordinary Differential Equations (Marita Thomas)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Ordinary differential equations arise in many applications from physics, chemistry, biology or economics. This seminar extends the topics that were covered in the Analysis III course, e.g., eigenvalue problems and stability theory will be addressed. 

• Special topics in Mathematics

  0084dB2.11
  • 19202001 Lecture
    Discrete Geometrie I (Christian Haase)
    Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Special topics in Pure Mathematics

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  • 19236101 Lecture
    Mathematisches Panorama (Anina Mischau, Sarah Wolf)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Comments

    This is for a course in German - Short explanation in English:

    Mathematical Panorama is a two-hour overview course for First-Semester students of Mathematics (in particular, but not only, for teacher students) that presents the wide field of modern Mathematics - its history, its topics, its problems, its methods, some basic concepts, applications, etc.

     

    Suggested reading

    • Günter M. Ziegler und Andreas Loos: Panorama der Mathematik, Springer-Spektrum 2018, in Vorbereitung (wird in Auszügen zur Verfügung gestellt)
    • Hans Wußing, 6000 Jahre Mathematik: Eine kulturgeschichtliche Zeitreise, Springer 2009
      • Band 1: Von den Anfängen bis Leibniz und Newton
      • Band 2: Von Euler bis zur Gegenwart
    • Heinz-Wilhelm Alten et al., 4000 Jahre Algebra, Springer 2008
    • Christoph J. Scriba, 5000 Jahre Geometrie, Springer 2009
    • Heinz Niels Jahnke, Geschichte der Analysis: Texte zur Didaktik der Mathematik, Spektrum 1999
    • Richard Courant und Herbert Robbins, What is Mathematics?, Oxford UP 1941 (deutsch: Springer 2010)
    • Phillip J. Davis, Reuben Hersh, The Mathematical Experience, Mariner Books 1999

  • 19236102 Practice seminar
    Übung zu: Mathematisches Panorama (Anina Mischau)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-24)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

• Functional Analysis

  0084dB2.2
  • 19201901 Lecture
    Functional Analysis (Dirk Werner)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    Content:
    Functional analysis is the branch of mathematics dealing with the study of normed (or general topological) vector spaces and continuous mappings between them. Thus, analysis, topology and algebra are linked.
    The course deals with Banach and Hilbert spaces, linear operators and functionals as well as spectral theory of compact operators.

    Target group: Students from the 3rd/4th semester on.

    Requirements: Good command of the material of the courses Analysis I/II and Linear Algebra I/II.

    Suggested reading

    Literatur:

    • Dirk Werner: Funktionalanalysis, 8. Auflage, Springer-Verlag 2018

  • 19201902 Practice seminar
    Tutorial: Functional Analysis (Dirk Werner)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Inhalt:
    Die Funktionalanalysis ist der Zweig der Mathematik, der sich mit der Untersuchung von normierten (oder allgemeiner topologischen) Vektorräumen und stetigen Abbildungen zwischen ihnen befasst. Hierbei werden Analysis, Topologie und Algebra verknüpft.
    Die Vorlesung behandelt Banach- und Hilberträume, lineare Operatoren und Funktionale sowie Spektraltheorie kompakter Operatoren.
    
    Zielgruppe: Studierende vom 4. Semester an.
    
    Voraussetzungen: Sicheres Beherrschen des Stoffs der Vorlesungen Analysis I/II und Lineare Algebra I/II.
    
    Literatur:

     

    • Dirk Werner: Funktionalanalysis, 6. Auflage, Springer-Verlag 2007, ISBN 978-3-540-72533-6
    • Hans Wilhelm Alt: Lineare Funktionalanalysis : eine anwendungsorientierte Einführung. 5. Auflage. Springer-Verlag, 2006, ISBN 3-540-34186-2
    • Harro Heuser: Funktionalanalysis: Theorie und Anwendung. 3. Auflage. Teubner-Verlag, 1992, ISBN 3-519-22206-X

     

• Probability and Statistics II

  0084dB2.4
  • 19212901 Lecture
    Stochastics II (Felix Höfling)
    Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I  and  Analysis I — III.

    Comments

    Contents:

    • Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
    • Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
    • martingales in discrete time: convergence, stopping theorems, inequalities;
    • Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

    Suggested reading

    • Klenke: Wahrscheinlichkeitstheorie
    • Durrett: Probability. Theory and Examples.

    Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
    Further literature will be given during the lecture.

  • 19212902 Practice seminar
    Practice seminar for Stochastics II (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt

     

     

    • This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
      More precisely, the course will cover the following aspects of probability theory:
    • Measure theory and the Lebesgue integral
    • Convergence of random variables and 0-1 laws
    • Generating functions: branching processes and characteristic functions
    • Markov chains
    • Introduction to martingales

     

     

• Algebra and Number Theroy

  0084dB2.5
  • 19200701 Lecture
    Algebra and Theory of Numbers (Alexander Schmitt)
    Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

    Subject matter:
    Selected topics from:

        Divisibility into rings (especially Z- and polynomial rings); residual classes and congruencies; modules and ideals
        Euclidean, principal ideal and factorial rings
        The quadratic law of reciprocity
        Primality tests and cryptography
        The structure of abel groups (or modules about main ideal rings)
        Symmetric function set
        Body extensions, Galois correspondence; constructions with compasses and rulers
        Non-Label groups (set of Lagrange, normal dividers, dissolvability, sylow groups)

  • 19200702 Practice seminar
    Practice seminar for Algebra and Theory of Numbers (Alexander Schmitt)
    Schedule: Mi 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Numerical Mathematics II

  0084dB3.4
  • 19202101 Lecture
    Basic Module: Numeric II (Robert Gruhlke)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

    Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

    Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Differential Geometry I

  0084dB3.5
  • 19202601 Lecture
    Differential Geometry I (Konrad Polthier)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Additional information / Pre-requisites

    For further information, see Lecture Homepage.

    Comments

    Topics of the lecture will be:

    • curves and surfaces in Euclidean space,
    • metrics and (Riemannian) manifolds,
    • surface tension, notions of curvature,
    • vector fields, tensors, covariant derivative
    • geodesic curves, exponential map,
    • Gauß-Bonnet theorem, topology,
    • connection to discrete differential geometry.

    This course is a BMS course and will be held in English on request.

    Prerequisits:

    Analysis I, II, III and Linear Algebra I, II

     

     

    Suggested reading

    Literature

    • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
    • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
    • J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
    • C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

  • 19202602 Practice seminar
    Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
    Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Communicating about Mathematics

  0162bA1.1
  • 19201510 Proseminar
    Undergraduate Seminar: Linar Algebra (Alexander Schmitt)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-10-13)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Comments

    
     

  • 19214010 Proseminar
    Undergraduate Seminar "Magic Tricks with Mathematical Background" (Ehrhard Behrends)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-10-20)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Magic tricks with a mathematical background will be analyzed.

    Suggested reading

    Literatur: Mein 2017 bei Springer Spektrum erschienenes Buch "Zaubern und Mathematik" sowie einige Originalarbeiten zum Thema.

  • 19240317 Seminar / Undergraduate Course
    Advancing mathematics with AI (Georg Loho)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    The course will probably be held in German. 

  • 19241710 Proseminar
    Proseminar Mathematics Panorama (Anna Maria Hartkopf)
    Schedule: Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-10-20)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Suggested reading

    1. Hans Wußing, 6000 Jahre Mathematik: Eine kulturgeschichtliche Zeitreise;
    2. Band 1: Von den Anfängen bis Leibniz und Newton, Band 2: Von Euler bis zur Gegenwart, Springer 2009
    3. Heinz-Wilhelm Alten et al., 4000 Jahre Algebra, Springer 2008
    4. Christoph J. Scriba, 5000 Jahre Geometrie, Springer 2009
    5. Heinz-Niels Jahnke, Geschichte der Analysis: Texte zur Didaktik der Mathematik, Spektrum 1999
    6. Richard Courant und Herbert Robbins, Was ist Mathematik?, Springer 2010
    7. Phillip J. Davis, Reuben Hersh, The Mathematical Experience, Mariner Books 1999
    8. Knoebel, Arthur; Laubenbacher, Reinhard; Lodder, Jerry; Pengelley, David
    9. Mathematical masterpieces, Springer 2007
    10. Laubenbacher, Reinhard; Pengelley, David, Mathematical expeditions. Chronicles by the explorers, Springer 1999
    11. sowie abhängig vom Thema

  • 19245910 Proseminar
    Undergraduate Seminar: Mathematical Games (Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Voraussetzungen: Mindestens 2-3 Anfangsvorlesungen in Mathematik, insbesondere Lineare Algebra, sollten besucht worden sein. Es wird nicht so sehr um die dort vermittelten Inhalte gehen, sondern vielmehr darum, mathematisches Arbeiten an der Hochschule (Definition, Satz, Beweis, Problemlösen) kennengelernt zu haben.

    Comments

    In diesem Proseminar werden Spiele behandelt, die in irgendeiner Form einen Bezug zu Mathematik haben. Beispiele sind Sudoku, Solitär, Lights Out, Dobble und Nim-Spiele.

    Das Hauptziel des Proseminars ist das Kennenlernen verschiedener Spiele und die Erarbeitung mathematischer Methoden, die zur Lösung zugehöriger Fragestellungen benutzt werden. Diese Methoden stammen aus verschiedensten Bereichen der Mathematik, etwa aus der Linearen Algebra oder der Kombinatorik.

    Die Aufgabe der Teilnehmenden ist die (angeleitete) Erarbeitung von Fachartikeln zu Spielen; diese Literatur ist in der Regel nur in englischer Sprache vorhanden. Dabei sollen Beweisideen verstanden und den anderen Teilnehmenden in einem Vortrag präsentiert werden. Die Einbindung der Zuhörenden ist sehr erwünscht.

    Es gibt eine verpflichtende Vorbesprechung am 25.02.2022 von 10-12 Uhr. Diese wird online stattfinden und ist über folgenden Link erreichbar: https://fu-berlin.webex.com/fu-berlin/j.php?MTID=mdf50fc829d3a738c52fdb93987207441

    Suggested reading

    Die Literatur wird bei der Vorbesprechung bekanntgegeben. Zur Einstimmung kann man bereits etwas in einem der Bände der Reihe Winning Ways for Your Mathematical Plays von Berlekamp, Conway und Guy schmökern.

    Unbedingt zur Seminarvorbereitung lesen:

    M. Lehn: Wie halte ich einen Seminarvortrag?

• Introductory Module: Differential Geometry I

  0280bA1.1
  • 19202601 Lecture
    Differential Geometry I (Konrad Polthier)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Additional information / Pre-requisites

    For further information, see Lecture Homepage.

    Comments

    Topics of the lecture will be:

    • curves and surfaces in Euclidean space,
    • metrics and (Riemannian) manifolds,
    • surface tension, notions of curvature,
    • vector fields, tensors, covariant derivative
    • geodesic curves, exponential map,
    • Gauß-Bonnet theorem, topology,
    • connection to discrete differential geometry.

    This course is a BMS course and will be held in English on request.

    Prerequisits:

    Analysis I, II, III and Linear Algebra I, II

     

     

    Suggested reading

    Literature

    • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
    • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
    • J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
    • C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

  • 19202602 Practice seminar
    Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
    Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Research Module: Differential Geometry

  0280bA1.4
  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier, Tillmann Kleiner)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

• Advanced Module: Algebra III

  0280bA2.3
  • 19222301 Lecture
    Advanced Module: Algebra III (Holger Reich)
    Schedule: Mo 12:00-14:00 (Class starts on: 2025-10-20)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    Course contents: a selection of the following topics

    • properties of morphisms (proper, projective, smooth)
    • divisors
    • (quasi-)coherent sheaves
    • cohomology
    • Hilbert functions

    further properties of morphisms (proper, integral, regular, smooth, étale, ...)

    • Grothendieck topologies
    • cohomology (Cech, étale, ...)

    Suggested reading

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

  • 19222302 Practice seminar
    Practice seminar for Advanced Module: Algebra III (Holger Reich)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A7/SR 031 (Arnimallee 7)
    

• Introductory Module: Discrete Mathematics II

  0280bA3.2
  • 19234401 Lecture
    Discrete Mathematics II - Optimization (Ralf Borndörfer)
    Schedule: Mo 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: Mo A6/SR 032 Seminarraum (Arnimallee 6), Do A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    Credit This course can be chosen as Discrete Mathematics II (DM II). If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module. Language This lecture is in English.

    Exam

    The exam takes place at the last lecture. The 2nd exam takes place in the last week of the summer holidays before the lectures resume.

    Comments

    This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

    Contents

    Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness
    Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
    Shortest Paths: nonnegative weights, general weights, all pairs
    Network Flows: Max-Flow-Min-Cut Theorem, augmenting paths, minimum cost flows, transport and allocation problems
    Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
    Foundations of linear optimization: Farkas Lemma, Duality Theorem
    Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
    Interior point and ellipsoid method: basics

    Audience

    This course is aimed at mathematics students with knowledge of discrete mathematics I, linear algebra and analysis. Some exercises require the use of a computer.

    Suggested reading

    M. Grötschel, Lineare Optimierung, eines der Vorlesungsskripte

    V. Chvátal, Linear Programming, Freeman 1983

    Additional

    Garey & Johnson, Computers and Intractability,  1979 (Complexity Theory)

    Bertsimas & Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

    Korte & Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

• Introductory Module: Discrete Geometry I

  0280bA3.3
  • 19202001 Lecture
    Discrete Geometrie I (Christian Haase)
    Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Advanced Module: Discrete Geometry III

  0280bA3.6
  • 19205901 Lecture
    Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
    
    Requirements: Preferably Discrete Geometry I and II.

    Comments

    This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):   1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or   2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or   3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or   4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

    Suggested reading

    Will be announced in class.

  • 19205902 Practice seminar
    Practice seminar for Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

• Introductory Module: Topology II

  0280bA4.2
  • 19206201 Lecture
    Basic Module: Topology II (Pavle Blagojevic)
    Schedule: Di 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

    Suggested reading

    Literatur

    • Hatcher, Allen: Algebraic Topology; Cambridge University Press.
    • http://www.math.cornell.edu/~hatcher/AT/ATpage.html
    • Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

• Research Module: Topology

  0280bA4.5
  • 19223811 Seminar
    Master Seminar Topology "L^2-Betti numbers" (N.N.)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of topology and group theory is required.

    Comments

    The Euler characteristic of finite CW-complexes is multiplicative under finite-sheeted coverings and it is homotopy invariant. These properties can be deduced from different descriptions:
    1. As the alternating sum of the numbers of cells, which are multiplicative but not homotopy invariant.
    2. As the alternating sum of Betti numbers, which are homotopy invariant but not multiplicative. The $n$-th Betti number of $X$ is the $\mathbb{Q}$-dimension of the homology $H_n(X;\mathbb{Q})$ with rational coefficients.
    3. As the alternating sum of $L^2$-Betti numbers, which enjoy the best features from both worlds: they are multiplicative and homotopy invariant. The $n$-th $L^2$-Betti number of $X$ is the von Neumann-dimension of the homology $H_n(X; \mathcal{N}\pi_1(X))$ with suitable coefficients.
    
    $L^2$-Betti numbers are meaningful topological invariants, as they obstruct the structures of mapping tori and $S^1$-actions. They also have applications to group theory by considering the $L^2$-Betti numbers of classifying spaces. Moreover, $L^2$-Betti numbers are related to famous open problems, such as the Hopf and Singer conjectures on the Euler characteristic of manifolds, and the Kaplansky conjecture on zero divisors in group rings.

    Detailed Information can be found on the Homepage of the seminar.

    Suggested reading

    This seminar will be an introduction to $L^2$-Betti numbers, following mostly
    the book by Holger Kammeyer.

• Introductory Module: Numerical Analysis II

  0280bA5.1
  • 19202101 Lecture
    Basic Module: Numeric II (Robert Gruhlke)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

    Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

    Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Introductory Module: Differential Equations II

  0280bA6.2
  • 19242001 Lecture
    Partial Differential Equations II (Erica Ipocoana)
    Schedule: Di 08:00-10:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    This course builds on the material of the course Partial Differential Equations I as taught in the previous summer term. Methods for linear partial differential equations will be deepened and extended to nonlinear partial differential equations. A central topic of the course is the theory of monotone and maximal monotone operators. 

     

  • 19242002 Practice seminar
    Tutorial Partial Differential Equations II (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Complementary Module: Selected Topics

  0280bA7.1
  • 19225101 Lecture
    Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mo 12:00-14:00, Di 12:00-14:00 (Class starts on: 2025-10-14)
    Location: SR A9
    

    Additional information / Pre-requisites

    Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

    Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

    Comments

    Program

    Polymer Physics: Structure and Dynamics

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Biological Membranes

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Introduction to Colloids and Liquid Crystals

    • Theory and Simulation

    Introduction to Hydrodynamic scale for large Biological Systems:

    • Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

    Suggested reading

    Basic Literature:

    1. Introduction to Polymer Physics by M. Doi
    2. Soft Matter Physics by M. Doi
    3. Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

  • 19234401 Lecture
    Discrete Mathematics II - Optimization (Ralf Borndörfer)
    Schedule: Mo 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: Mo A6/SR 032 Seminarraum (Arnimallee 6), Do A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    Credit This course can be chosen as Discrete Mathematics II (DM II). If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module. Language This lecture is in English.

    Exam

    The exam takes place at the last lecture. The 2nd exam takes place in the last week of the summer holidays before the lectures resume.

    Comments

    This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

    Contents

    Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness
    Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
    Shortest Paths: nonnegative weights, general weights, all pairs
    Network Flows: Max-Flow-Min-Cut Theorem, augmenting paths, minimum cost flows, transport and allocation problems
    Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
    Foundations of linear optimization: Farkas Lemma, Duality Theorem
    Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
    Interior point and ellipsoid method: basics

    Audience

    This course is aimed at mathematics students with knowledge of discrete mathematics I, linear algebra and analysis. Some exercises require the use of a computer.

    Suggested reading

    M. Grötschel, Lineare Optimierung, eines der Vorlesungsskripte

    V. Chvátal, Linear Programming, Freeman 1983

    Additional

    Garey & Johnson, Computers and Intractability,  1979 (Complexity Theory)

    Bertsimas & Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

    Korte & Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

  • 19225102 Practice seminar
    Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: SR A9
    

• Complementary Module: Selected Research Topics

  0280bA7.2
  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content:
    This course considers the fundamental equation of fluid dynamics - the incompressible Navier-Stokes equations. These partial differential equations are nonlinear, not symmetric, and they are a coupled systems of two equations. The dominating term is generally the convective term. All these features lead to difficulties in the numerical simulation of the Navier-Stokes equations. The course will start with a derivation of these equations and an overview about results from the analysis will be given. The difficulties in the numerical simulation of the Navier-Stokes equations can be studied separately at simpler equations. This course will consider only stationary equations. The time-dependent equations, in particular turbulent flows, will be the topic of the next semester.
    
    Requirements:
    Basic knowledge on numerical methods for partial differential equations, in particular finite element methods (Numerical Mathematics 3)

  • 19207102 Practice seminar
    Tutorials for Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

• Complementary Module: Research Seminar

  0280bA7.5
  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier, Tillmann Kleiner)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

  • 19223811 Seminar
    Master Seminar Topology "L^2-Betti numbers" (N.N.)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of topology and group theory is required.

    Comments

    The Euler characteristic of finite CW-complexes is multiplicative under finite-sheeted coverings and it is homotopy invariant. These properties can be deduced from different descriptions:
    1. As the alternating sum of the numbers of cells, which are multiplicative but not homotopy invariant.
    2. As the alternating sum of Betti numbers, which are homotopy invariant but not multiplicative. The $n$-th Betti number of $X$ is the $\mathbb{Q}$-dimension of the homology $H_n(X;\mathbb{Q})$ with rational coefficients.
    3. As the alternating sum of $L^2$-Betti numbers, which enjoy the best features from both worlds: they are multiplicative and homotopy invariant. The $n$-th $L^2$-Betti number of $X$ is the von Neumann-dimension of the homology $H_n(X; \mathcal{N}\pi_1(X))$ with suitable coefficients.
    
    $L^2$-Betti numbers are meaningful topological invariants, as they obstruct the structures of mapping tori and $S^1$-actions. They also have applications to group theory by considering the $L^2$-Betti numbers of classifying spaces. Moreover, $L^2$-Betti numbers are related to famous open problems, such as the Hopf and Singer conjectures on the Euler characteristic of manifolds, and the Kaplansky conjecture on zero divisors in group rings.

    Detailed Information can be found on the Homepage of the seminar.

    Suggested reading

    This seminar will be an introduction to $L^2$-Betti numbers, following mostly
    the book by Holger Kammeyer.

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
    Location: SR A9
    

    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

• Complementary Module: Probability and Statistics II

  0280bA7.7
  • 19212901 Lecture
    Stochastics II (Felix Höfling)
    Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I  and  Analysis I — III.

    Comments

    Contents:

    • Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
    • Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
    • martingales in discrete time: convergence, stopping theorems, inequalities;
    • Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

    Suggested reading

    • Klenke: Wahrscheinlichkeitstheorie
    • Durrett: Probability. Theory and Examples.

    Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
    Further literature will be given during the lecture.

  • 19212902 Practice seminar
    Practice seminar for Stochastics II (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt

     

     

    • This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
      More precisely, the course will cover the following aspects of probability theory:
    • Measure theory and the Lebesgue integral
    • Convergence of random variables and 0-1 laws
    • Generating functions: branching processes and characteristic functions
    • Markov chains
    • Introduction to martingales

     

     

• Complementary Module: BMS Fridays

  0280bA7.8
  • 19223111 Seminar
    BMS Fridays (Holger Reich)
    Schedule: Fr 14:00-18:00 (Class starts on: 2025-10-17)
    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…?

  0280bA7.9
  • 19217311 Seminar
    PhD Seminar "What is...?" (Holger Reich)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    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

• Introductory Module: Numerical Mathematics II

  0280cA1.11
  • 19202101 Lecture
    Basic Module: Numeric II (Robert Gruhlke)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

    Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

    Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Introductory Module: Partial Differential Equations II

  0280cA1.14
  • 19242001 Lecture
    Partial Differential Equations II (Erica Ipocoana)
    Schedule: Di 08:00-10:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    This course builds on the material of the course Partial Differential Equations I as taught in the previous summer term. Methods for linear partial differential equations will be deepened and extended to nonlinear partial differential equations. A central topic of the course is the theory of monotone and maximal monotone operators. 

     

  • 19242002 Practice seminar
    Tutorial Partial Differential Equations II (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Introductory Module: Probability and Statistics II

  0280cA1.15
  • 19212901 Lecture
    Stochastics II (Felix Höfling)
    Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I  and  Analysis I — III.

    Comments

    Contents:

    • Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
    • Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
    • martingales in discrete time: convergence, stopping theorems, inequalities;
    • Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

    Suggested reading

    • Klenke: Wahrscheinlichkeitstheorie
    • Durrett: Probability. Theory and Examples.

    Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
    Further literature will be given during the lecture.

  • 19212902 Practice seminar
    Practice seminar for Stochastics II (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt

     

     

    • This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
      More precisely, the course will cover the following aspects of probability theory:
    • Measure theory and the Lebesgue integral
    • Convergence of random variables and 0-1 laws
    • Generating functions: branching processes and characteristic functions
    • Markov chains
    • Introduction to martingales

     

     

• Introductory Module: Topology II

  0280cA1.18
  • 19206201 Lecture
    Basic Module: Topology II (Pavle Blagojevic)
    Schedule: Di 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

    Suggested reading

    Literatur

    • Hatcher, Allen: Algebraic Topology; Cambridge University Press.
    • http://www.math.cornell.edu/~hatcher/AT/ATpage.html
    • Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

• Introductory Module: Differential Geometry I

  0280cA1.3
  • 19202601 Lecture
    Differential Geometry I (Konrad Polthier)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Additional information / Pre-requisites

    For further information, see Lecture Homepage.

    Comments

    Topics of the lecture will be:

    • curves and surfaces in Euclidean space,
    • metrics and (Riemannian) manifolds,
    • surface tension, notions of curvature,
    • vector fields, tensors, covariant derivative
    • geodesic curves, exponential map,
    • Gauß-Bonnet theorem, topology,
    • connection to discrete differential geometry.

    This course is a BMS course and will be held in English on request.

    Prerequisits:

    Analysis I, II, III and Linear Algebra I, II

     

     

    Suggested reading

    Literature

    • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
    • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
    • J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
    • C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

  • 19202602 Practice seminar
    Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
    Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Introductory Module: Discrete Geometry I

  0280cA1.5
  • 19202001 Lecture
    Discrete Geometrie I (Christian Haase)
    Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Introductory Module: Discrete Mathematics II

  0280cA1.8
  • 19234401 Lecture
    Discrete Mathematics II - Optimization (Ralf Borndörfer)
    Schedule: Mo 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: Mo A6/SR 032 Seminarraum (Arnimallee 6), Do A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    Credit This course can be chosen as Discrete Mathematics II (DM II). If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module. Language This lecture is in English.

    Exam

    The exam takes place at the last lecture. The 2nd exam takes place in the last week of the summer holidays before the lectures resume.

    Comments

    This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

    Contents

    Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness
    Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
    Shortest Paths: nonnegative weights, general weights, all pairs
    Network Flows: Max-Flow-Min-Cut Theorem, augmenting paths, minimum cost flows, transport and allocation problems
    Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
    Foundations of linear optimization: Farkas Lemma, Duality Theorem
    Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
    Interior point and ellipsoid method: basics

    Audience

    This course is aimed at mathematics students with knowledge of discrete mathematics I, linear algebra and analysis. Some exercises require the use of a computer.

    Suggested reading

    M. Grötschel, Lineare Optimierung, eines der Vorlesungsskripte

    V. Chvátal, Linear Programming, Freeman 1983

    Additional

    Garey & Johnson, Computers and Intractability,  1979 (Complexity Theory)

    Bertsimas & Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

    Korte & Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

• Advanced Module: Algebra III

  0280cA2.1
  • 19222301 Lecture
    Advanced Module: Algebra III (Holger Reich)
    Schedule: Mo 12:00-14:00 (Class starts on: 2025-10-20)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    Course contents: a selection of the following topics

    • properties of morphisms (proper, projective, smooth)
    • divisors
    • (quasi-)coherent sheaves
    • cohomology
    • Hilbert functions

    further properties of morphisms (proper, integral, regular, smooth, étale, ...)

    • Grothendieck topologies
    • cohomology (Cech, étale, ...)

    Suggested reading

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

  • 19222302 Practice seminar
    Practice seminar for Advanced Module: Algebra III (Holger Reich)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A7/SR 031 (Arnimallee 7)
    

• Advanced Module: Discrete Geometry III

  0280cA2.3
  • 19205901 Lecture
    Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
    
    Requirements: Preferably Discrete Geometry I and II.

    Comments

    This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):   1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or   2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or   3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or   4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

    Suggested reading

    Will be announced in class.

  • 19205902 Practice seminar
    Practice seminar for Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

• Advanced Module: Numerical Mathematics IV

  0280cA2.6
  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content:
    This course considers the fundamental equation of fluid dynamics - the incompressible Navier-Stokes equations. These partial differential equations are nonlinear, not symmetric, and they are a coupled systems of two equations. The dominating term is generally the convective term. All these features lead to difficulties in the numerical simulation of the Navier-Stokes equations. The course will start with a derivation of these equations and an overview about results from the analysis will be given. The difficulties in the numerical simulation of the Navier-Stokes equations can be studied separately at simpler equations. This course will consider only stationary equations. The time-dependent equations, in particular turbulent flows, will be the topic of the next semester.
    
    Requirements:
    Basic knowledge on numerical methods for partial differential equations, in particular finite element methods (Numerical Mathematics 3)

  • 19207102 Practice seminar
    Tutorials for Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

• Specialization Module: Master's Seminar on Differential Geometry

  0280cA3.2
  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier, Tillmann Kleiner)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

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

  0280cA3.7
  • 19247111 Seminar
    Ordinary Differential Equations (Marita Thomas)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Ordinary differential equations arise in many applications from physics, chemistry, biology or economics. This seminar extends the topics that were covered in the Analysis III course, e.g., eigenvalue problems and stability theory will be addressed. 

• Specialization Module: Master’s Seminar on Topology

  0280cA3.9
  • 19223811 Seminar
    Master Seminar Topology "L^2-Betti numbers" (N.N.)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of topology and group theory is required.

    Comments

    The Euler characteristic of finite CW-complexes is multiplicative under finite-sheeted coverings and it is homotopy invariant. These properties can be deduced from different descriptions:
    1. As the alternating sum of the numbers of cells, which are multiplicative but not homotopy invariant.
    2. As the alternating sum of Betti numbers, which are homotopy invariant but not multiplicative. The $n$-th Betti number of $X$ is the $\mathbb{Q}$-dimension of the homology $H_n(X;\mathbb{Q})$ with rational coefficients.
    3. As the alternating sum of $L^2$-Betti numbers, which enjoy the best features from both worlds: they are multiplicative and homotopy invariant. The $n$-th $L^2$-Betti number of $X$ is the von Neumann-dimension of the homology $H_n(X; \mathcal{N}\pi_1(X))$ with suitable coefficients.
    
    $L^2$-Betti numbers are meaningful topological invariants, as they obstruct the structures of mapping tori and $S^1$-actions. They also have applications to group theory by considering the $L^2$-Betti numbers of classifying spaces. Moreover, $L^2$-Betti numbers are related to famous open problems, such as the Hopf and Singer conjectures on the Euler characteristic of manifolds, and the Kaplansky conjecture on zero divisors in group rings.

    Detailed Information can be found on the Homepage of the seminar.

    Suggested reading

    This seminar will be an introduction to $L^2$-Betti numbers, following mostly
    the book by Holger Kammeyer.

• Complementary Module: Selected Topics A

  0280cA4.1
  • 19202001 Lecture
    Discrete Geometrie I (Christian Haase)
    Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202101 Lecture
    Basic Module: Numeric II (Robert Gruhlke)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

    Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

    Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

  • 19202601 Lecture
    Differential Geometry I (Konrad Polthier)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Additional information / Pre-requisites

    For further information, see Lecture Homepage.

    Comments

    Topics of the lecture will be:

    • curves and surfaces in Euclidean space,
    • metrics and (Riemannian) manifolds,
    • surface tension, notions of curvature,
    • vector fields, tensors, covariant derivative
    • geodesic curves, exponential map,
    • Gauß-Bonnet theorem, topology,
    • connection to discrete differential geometry.

    This course is a BMS course and will be held in English on request.

    Prerequisits:

    Analysis I, II, III and Linear Algebra I, II

     

     

    Suggested reading

    Literature

    • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
    • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
    • J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
    • C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

  • 19206201 Lecture
    Basic Module: Topology II (Pavle Blagojevic)
    Schedule: Di 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

    Suggested reading

    Literatur

    • Hatcher, Allen: Algebraic Topology; Cambridge University Press.
    • http://www.math.cornell.edu/~hatcher/AT/ATpage.html
    • Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

  • 19212901 Lecture
    Stochastics II (Felix Höfling)
    Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I  and  Analysis I — III.

    Comments

    Contents:

    • Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
    • Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
    • martingales in discrete time: convergence, stopping theorems, inequalities;
    • Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

    Suggested reading

    • Klenke: Wahrscheinlichkeitstheorie
    • Durrett: Probability. Theory and Examples.

    Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
    Further literature will be given during the lecture.

  • 19225101 Lecture
    Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mo 12:00-14:00, Di 12:00-14:00 (Class starts on: 2025-10-14)
    Location: SR A9
    

    Additional information / Pre-requisites

    Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

    Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

    Comments

    Program

    Polymer Physics: Structure and Dynamics

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Biological Membranes

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Introduction to Colloids and Liquid Crystals

    • Theory and Simulation

    Introduction to Hydrodynamic scale for large Biological Systems:

    • Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

    Suggested reading

    Basic Literature:

    1. Introduction to Polymer Physics by M. Doi
    2. Soft Matter Physics by M. Doi
    3. Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

  • 19234401 Lecture
    Discrete Mathematics II - Optimization (Ralf Borndörfer)
    Schedule: Mo 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: Mo A6/SR 032 Seminarraum (Arnimallee 6), Do A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    Credit This course can be chosen as Discrete Mathematics II (DM II). If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module. Language This lecture is in English.

    Exam

    The exam takes place at the last lecture. The 2nd exam takes place in the last week of the summer holidays before the lectures resume.

    Comments

    This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

    Contents

    Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness
    Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
    Shortest Paths: nonnegative weights, general weights, all pairs
    Network Flows: Max-Flow-Min-Cut Theorem, augmenting paths, minimum cost flows, transport and allocation problems
    Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
    Foundations of linear optimization: Farkas Lemma, Duality Theorem
    Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
    Interior point and ellipsoid method: basics

    Audience

    This course is aimed at mathematics students with knowledge of discrete mathematics I, linear algebra and analysis. Some exercises require the use of a computer.

    Suggested reading

    M. Grötschel, Lineare Optimierung, eines der Vorlesungsskripte

    V. Chvátal, Linear Programming, Freeman 1983

    Additional

    Garey & Johnson, Computers and Intractability,  1979 (Complexity Theory)

    Bertsimas & Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

    Korte & Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

  • 19242001 Lecture
    Partial Differential Equations II (Erica Ipocoana)
    Schedule: Di 08:00-10:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    This course builds on the material of the course Partial Differential Equations I as taught in the previous summer term. Methods for linear partial differential equations will be deepened and extended to nonlinear partial differential equations. A central topic of the course is the theory of monotone and maximal monotone operators. 

     

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19202602 Practice seminar
    Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
    Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19212902 Practice seminar
    Practice seminar for Stochastics II (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt

     

     

    • This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
      More precisely, the course will cover the following aspects of probability theory:
    • Measure theory and the Lebesgue integral
    • Convergence of random variables and 0-1 laws
    • Generating functions: branching processes and characteristic functions
    • Markov chains
    • Introduction to martingales

     

     

  • 19225102 Practice seminar
    Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: SR A9
    
  • 19242002 Practice seminar
    Tutorial Partial Differential Equations II (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Complementary Module: Selected Topics B

  0280cA4.2
  • 19202001 Lecture
    Discrete Geometrie I (Christian Haase)
    Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202101 Lecture
    Basic Module: Numeric II (Robert Gruhlke)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

    Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

    Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

  • 19202601 Lecture
    Differential Geometry I (Konrad Polthier)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Additional information / Pre-requisites

    For further information, see Lecture Homepage.

    Comments

    Topics of the lecture will be:

    • curves and surfaces in Euclidean space,
    • metrics and (Riemannian) manifolds,
    • surface tension, notions of curvature,
    • vector fields, tensors, covariant derivative
    • geodesic curves, exponential map,
    • Gauß-Bonnet theorem, topology,
    • connection to discrete differential geometry.

    This course is a BMS course and will be held in English on request.

    Prerequisits:

    Analysis I, II, III and Linear Algebra I, II

     

     

    Suggested reading

    Literature

    • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
    • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
    • J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
    • C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

  • 19206201 Lecture
    Basic Module: Topology II (Pavle Blagojevic)
    Schedule: Di 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

    Suggested reading

    Literatur

    • Hatcher, Allen: Algebraic Topology; Cambridge University Press.
    • http://www.math.cornell.edu/~hatcher/AT/ATpage.html
    • Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

  • 19212901 Lecture
    Stochastics II (Felix Höfling)
    Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I  and  Analysis I — III.

    Comments

    Contents:

    • Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
    • Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
    • martingales in discrete time: convergence, stopping theorems, inequalities;
    • Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

    Suggested reading

    • Klenke: Wahrscheinlichkeitstheorie
    • Durrett: Probability. Theory and Examples.

    Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
    Further literature will be given during the lecture.

  • 19225101 Lecture
    Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mo 12:00-14:00, Di 12:00-14:00 (Class starts on: 2025-10-14)
    Location: SR A9
    

    Additional information / Pre-requisites

    Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

    Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

    Comments

    Program

    Polymer Physics: Structure and Dynamics

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Biological Membranes

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Introduction to Colloids and Liquid Crystals

    • Theory and Simulation

    Introduction to Hydrodynamic scale for large Biological Systems:

    • Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

    Suggested reading

    Basic Literature:

    1. Introduction to Polymer Physics by M. Doi
    2. Soft Matter Physics by M. Doi
    3. Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

  • 19234401 Lecture
    Discrete Mathematics II - Optimization (Ralf Borndörfer)
    Schedule: Mo 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: Mo A6/SR 032 Seminarraum (Arnimallee 6), Do A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    Credit This course can be chosen as Discrete Mathematics II (DM II). If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module. Language This lecture is in English.

    Exam

    The exam takes place at the last lecture. The 2nd exam takes place in the last week of the summer holidays before the lectures resume.

    Comments

    This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

    Contents

    Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness
    Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
    Shortest Paths: nonnegative weights, general weights, all pairs
    Network Flows: Max-Flow-Min-Cut Theorem, augmenting paths, minimum cost flows, transport and allocation problems
    Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
    Foundations of linear optimization: Farkas Lemma, Duality Theorem
    Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
    Interior point and ellipsoid method: basics

    Audience

    This course is aimed at mathematics students with knowledge of discrete mathematics I, linear algebra and analysis. Some exercises require the use of a computer.

    Suggested reading

    M. Grötschel, Lineare Optimierung, eines der Vorlesungsskripte

    V. Chvátal, Linear Programming, Freeman 1983

    Additional

    Garey & Johnson, Computers and Intractability,  1979 (Complexity Theory)

    Bertsimas & Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

    Korte & Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

  • 19242001 Lecture
    Partial Differential Equations II (Erica Ipocoana)
    Schedule: Di 08:00-10:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    This course builds on the material of the course Partial Differential Equations I as taught in the previous summer term. Methods for linear partial differential equations will be deepened and extended to nonlinear partial differential equations. A central topic of the course is the theory of monotone and maximal monotone operators. 

     

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19202602 Practice seminar
    Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
    Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19212902 Practice seminar
    Practice seminar for Stochastics II (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt

     

     

    • This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
      More precisely, the course will cover the following aspects of probability theory:
    • Measure theory and the Lebesgue integral
    • Convergence of random variables and 0-1 laws
    • Generating functions: branching processes and characteristic functions
    • Markov chains
    • Introduction to martingales

     

     

  • 19225102 Practice seminar
    Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: SR A9
    
  • 19242002 Practice seminar
    Tutorial Partial Differential Equations II (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Complementary Module: Selected Topics C

  0280cA4.3
  • 19202001 Lecture
    Discrete Geometrie I (Christian Haase)
    Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202101 Lecture
    Basic Module: Numeric II (Robert Gruhlke)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

    Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

    Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

  • 19202601 Lecture
    Differential Geometry I (Konrad Polthier)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Additional information / Pre-requisites

    For further information, see Lecture Homepage.

    Comments

    Topics of the lecture will be:

    • curves and surfaces in Euclidean space,
    • metrics and (Riemannian) manifolds,
    • surface tension, notions of curvature,
    • vector fields, tensors, covariant derivative
    • geodesic curves, exponential map,
    • Gauß-Bonnet theorem, topology,
    • connection to discrete differential geometry.

    This course is a BMS course and will be held in English on request.

    Prerequisits:

    Analysis I, II, III and Linear Algebra I, II

     

     

    Suggested reading

    Literature

    • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
    • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
    • J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
    • C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

  • 19206201 Lecture
    Basic Module: Topology II (Pavle Blagojevic)
    Schedule: Di 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

    Suggested reading

    Literatur

    • Hatcher, Allen: Algebraic Topology; Cambridge University Press.
    • http://www.math.cornell.edu/~hatcher/AT/ATpage.html
    • Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

  • 19212901 Lecture
    Stochastics II (Felix Höfling)
    Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I  and  Analysis I — III.

    Comments

    Contents:

    • Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
    • Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
    • martingales in discrete time: convergence, stopping theorems, inequalities;
    • Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

    Suggested reading

    • Klenke: Wahrscheinlichkeitstheorie
    • Durrett: Probability. Theory and Examples.

    Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
    Further literature will be given during the lecture.

  • 19225101 Lecture
    Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mo 12:00-14:00, Di 12:00-14:00 (Class starts on: 2025-10-14)
    Location: SR A9
    

    Additional information / Pre-requisites

    Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

    Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

    Comments

    Program

    Polymer Physics: Structure and Dynamics

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Biological Membranes

    • (a) Theoretical/analytic approaches
    • (b) Physical and chemical Modeling
    • (c) Simulation

    Introduction to Colloids and Liquid Crystals

    • Theory and Simulation

    Introduction to Hydrodynamic scale for large Biological Systems:

    • Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

    Suggested reading

    Basic Literature:

    1. Introduction to Polymer Physics by M. Doi
    2. Soft Matter Physics by M. Doi
    3. Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

  • 19234401 Lecture
    Discrete Mathematics II - Optimization (Ralf Borndörfer)
    Schedule: Mo 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: Mo A6/SR 032 Seminarraum (Arnimallee 6), Do A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    Credit This course can be chosen as Discrete Mathematics II (DM II). If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module. Language This lecture is in English.

    Exam

    The exam takes place at the last lecture. The 2nd exam takes place in the last week of the summer holidays before the lectures resume.

    Comments

    This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

    Contents

    Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness
    Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
    Shortest Paths: nonnegative weights, general weights, all pairs
    Network Flows: Max-Flow-Min-Cut Theorem, augmenting paths, minimum cost flows, transport and allocation problems
    Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
    Foundations of linear optimization: Farkas Lemma, Duality Theorem
    Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
    Interior point and ellipsoid method: basics

    Audience

    This course is aimed at mathematics students with knowledge of discrete mathematics I, linear algebra and analysis. Some exercises require the use of a computer.

    Suggested reading

    M. Grötschel, Lineare Optimierung, eines der Vorlesungsskripte

    V. Chvátal, Linear Programming, Freeman 1983

    Additional

    Garey & Johnson, Computers and Intractability,  1979 (Complexity Theory)

    Bertsimas & Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

    Korte & Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

  • 19242001 Lecture
    Partial Differential Equations II (Erica Ipocoana)
    Schedule: Di 08:00-10:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    This course builds on the material of the course Partial Differential Equations I as taught in the previous summer term. Methods for linear partial differential equations will be deepened and extended to nonlinear partial differential equations. A central topic of the course is the theory of monotone and maximal monotone operators. 

     

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19202602 Practice seminar
    Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
    Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19212902 Practice seminar
    Practice seminar for Stochastics II (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt

     

     

    • This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
      More precisely, the course will cover the following aspects of probability theory:
    • Measure theory and the Lebesgue integral
    • Convergence of random variables and 0-1 laws
    • Generating functions: branching processes and characteristic functions
    • Markov chains
    • Introduction to martingales

     

     

  • 19225102 Practice seminar
    Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-10-15)
    Location: SR A9
    
  • 19242002 Practice seminar
    Tutorial Partial Differential Equations II (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Complementary Module: Specific Aspects A

  0280cA4.4
  • 19205901 Lecture
    Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
    
    Requirements: Preferably Discrete Geometry I and II.

    Comments

    This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):   1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or   2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or   3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or   4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

    Suggested reading

    Will be announced in class.

  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content:
    This course considers the fundamental equation of fluid dynamics - the incompressible Navier-Stokes equations. These partial differential equations are nonlinear, not symmetric, and they are a coupled systems of two equations. The dominating term is generally the convective term. All these features lead to difficulties in the numerical simulation of the Navier-Stokes equations. The course will start with a derivation of these equations and an overview about results from the analysis will be given. The difficulties in the numerical simulation of the Navier-Stokes equations can be studied separately at simpler equations. This course will consider only stationary equations. The time-dependent equations, in particular turbulent flows, will be the topic of the next semester.
    
    Requirements:
    Basic knowledge on numerical methods for partial differential equations, in particular finite element methods (Numerical Mathematics 3)

  • 19222301 Lecture
    Advanced Module: Algebra III (Holger Reich)
    Schedule: Mo 12:00-14:00 (Class starts on: 2025-10-20)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    Course contents: a selection of the following topics

    • properties of morphisms (proper, projective, smooth)
    • divisors
    • (quasi-)coherent sheaves
    • cohomology
    • Hilbert functions

    further properties of morphisms (proper, integral, regular, smooth, étale, ...)

    • Grothendieck topologies
    • cohomology (Cech, étale, ...)

    Suggested reading

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

  • 19205902 Practice seminar
    Practice seminar for Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19207102 Practice seminar
    Tutorials for Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19222302 Practice seminar
    Practice seminar for Advanced Module: Algebra III (Holger Reich)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A7/SR 031 (Arnimallee 7)
    

• Complementary Module: Specific Aspects B

  0280cA4.5
  • 19205901 Lecture
    Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
    
    Requirements: Preferably Discrete Geometry I and II.

    Comments

    This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):   1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or   2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or   3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or   4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

    Suggested reading

    Will be announced in class.

  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content:
    This course considers the fundamental equation of fluid dynamics - the incompressible Navier-Stokes equations. These partial differential equations are nonlinear, not symmetric, and they are a coupled systems of two equations. The dominating term is generally the convective term. All these features lead to difficulties in the numerical simulation of the Navier-Stokes equations. The course will start with a derivation of these equations and an overview about results from the analysis will be given. The difficulties in the numerical simulation of the Navier-Stokes equations can be studied separately at simpler equations. This course will consider only stationary equations. The time-dependent equations, in particular turbulent flows, will be the topic of the next semester.
    
    Requirements:
    Basic knowledge on numerical methods for partial differential equations, in particular finite element methods (Numerical Mathematics 3)

  • 19222301 Lecture
    Advanced Module: Algebra III (Holger Reich)
    Schedule: Mo 12:00-14:00 (Class starts on: 2025-10-20)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    Course contents: a selection of the following topics

    • properties of morphisms (proper, projective, smooth)
    • divisors
    • (quasi-)coherent sheaves
    • cohomology
    • Hilbert functions

    further properties of morphisms (proper, integral, regular, smooth, étale, ...)

    • Grothendieck topologies
    • cohomology (Cech, étale, ...)

    Suggested reading

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

  • 19205902 Practice seminar
    Practice seminar for Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19207102 Practice seminar
    Tutorials for Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19222302 Practice seminar
    Practice seminar for Advanced Module: Algebra III (Holger Reich)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A7/SR 031 (Arnimallee 7)
    

• Complementary Module: Specific Aspects C

  0280cA4.6
  • 19205901 Lecture
    Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
    
    Requirements: Preferably Discrete Geometry I and II.

    Comments

    This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):   1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or   2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or   3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or   4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

    Suggested reading

    Will be announced in class.

  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-10-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Content:
    This course considers the fundamental equation of fluid dynamics - the incompressible Navier-Stokes equations. These partial differential equations are nonlinear, not symmetric, and they are a coupled systems of two equations. The dominating term is generally the convective term. All these features lead to difficulties in the numerical simulation of the Navier-Stokes equations. The course will start with a derivation of these equations and an overview about results from the analysis will be given. The difficulties in the numerical simulation of the Navier-Stokes equations can be studied separately at simpler equations. This course will consider only stationary equations. The time-dependent equations, in particular turbulent flows, will be the topic of the next semester.
    
    Requirements:
    Basic knowledge on numerical methods for partial differential equations, in particular finite element methods (Numerical Mathematics 3)

  • 19222301 Lecture
    Advanced Module: Algebra III (Holger Reich)
    Schedule: Mo 12:00-14:00 (Class starts on: 2025-10-20)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    Course contents: a selection of the following topics

    • properties of morphisms (proper, projective, smooth)
    • divisors
    • (quasi-)coherent sheaves
    • cohomology
    • Hilbert functions

    further properties of morphisms (proper, integral, regular, smooth, étale, ...)

    • Grothendieck topologies
    • cohomology (Cech, étale, ...)

    Suggested reading

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

  • 19205902 Practice seminar
    Practice seminar for Advanced Module: Discrete Geometry III (N.N.)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19207102 Practice seminar
    Tutorials for Partial differential equations with multiple scales: Theory and computation (Juliane Rosemeier)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19222302 Practice seminar
    Practice seminar for Advanced Module: Algebra III (Holger Reich)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A7/SR 031 (Arnimallee 7)
    

• Complementary Module: Current Research Topics A

  0280cA4.7
  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier, Tillmann Kleiner)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

  • 19223811 Seminar
    Master Seminar Topology "L^2-Betti numbers" (N.N.)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of topology and group theory is required.

    Comments

    The Euler characteristic of finite CW-complexes is multiplicative under finite-sheeted coverings and it is homotopy invariant. These properties can be deduced from different descriptions:
    1. As the alternating sum of the numbers of cells, which are multiplicative but not homotopy invariant.
    2. As the alternating sum of Betti numbers, which are homotopy invariant but not multiplicative. The $n$-th Betti number of $X$ is the $\mathbb{Q}$-dimension of the homology $H_n(X;\mathbb{Q})$ with rational coefficients.
    3. As the alternating sum of $L^2$-Betti numbers, which enjoy the best features from both worlds: they are multiplicative and homotopy invariant. The $n$-th $L^2$-Betti number of $X$ is the von Neumann-dimension of the homology $H_n(X; \mathcal{N}\pi_1(X))$ with suitable coefficients.
    
    $L^2$-Betti numbers are meaningful topological invariants, as they obstruct the structures of mapping tori and $S^1$-actions. They also have applications to group theory by considering the $L^2$-Betti numbers of classifying spaces. Moreover, $L^2$-Betti numbers are related to famous open problems, such as the Hopf and Singer conjectures on the Euler characteristic of manifolds, and the Kaplansky conjecture on zero divisors in group rings.

    Detailed Information can be found on the Homepage of the seminar.

    Suggested reading

    This seminar will be an introduction to $L^2$-Betti numbers, following mostly
    the book by Holger Kammeyer.

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
    Location: SR A9
    

    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

  • 19247111 Seminar
    Ordinary Differential Equations (Marita Thomas)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Ordinary differential equations arise in many applications from physics, chemistry, biology or economics. This seminar extends the topics that were covered in the Analysis III course, e.g., eigenvalue problems and stability theory will be addressed. 

• Complementary Module: Current Research Topics B

  0280cA4.8
  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier, Tillmann Kleiner)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

  • 19223811 Seminar
    Master Seminar Topology "L^2-Betti numbers" (N.N.)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of topology and group theory is required.

    Comments

    The Euler characteristic of finite CW-complexes is multiplicative under finite-sheeted coverings and it is homotopy invariant. These properties can be deduced from different descriptions:
    1. As the alternating sum of the numbers of cells, which are multiplicative but not homotopy invariant.
    2. As the alternating sum of Betti numbers, which are homotopy invariant but not multiplicative. The $n$-th Betti number of $X$ is the $\mathbb{Q}$-dimension of the homology $H_n(X;\mathbb{Q})$ with rational coefficients.
    3. As the alternating sum of $L^2$-Betti numbers, which enjoy the best features from both worlds: they are multiplicative and homotopy invariant. The $n$-th $L^2$-Betti number of $X$ is the von Neumann-dimension of the homology $H_n(X; \mathcal{N}\pi_1(X))$ with suitable coefficients.
    
    $L^2$-Betti numbers are meaningful topological invariants, as they obstruct the structures of mapping tori and $S^1$-actions. They also have applications to group theory by considering the $L^2$-Betti numbers of classifying spaces. Moreover, $L^2$-Betti numbers are related to famous open problems, such as the Hopf and Singer conjectures on the Euler characteristic of manifolds, and the Kaplansky conjecture on zero divisors in group rings.

    Detailed Information can be found on the Homepage of the seminar.

    Suggested reading

    This seminar will be an introduction to $L^2$-Betti numbers, following mostly
    the book by Holger Kammeyer.

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
    Location: SR A9
    

    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

  • 19247111 Seminar
    Ordinary Differential Equations (Marita Thomas)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Ordinary differential equations arise in many applications from physics, chemistry, biology or economics. This seminar extends the topics that were covered in the Analysis III course, e.g., eigenvalue problems and stability theory will be addressed. 

• Complementary Module: Current Research Topics C

  0280cA4.9
  • 19214411 Seminar
    Research Module: Differential Geometrie (Konrad Polthier, Tillmann Kleiner)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In this seminar, differential geometric topics will be independently developed based on current research and presented in the form of a talk.
    
    Particular emphasis is placed on the concrete implementation of differential geometric concepts in application scenarios and the questions of discretization and implementation.
    
    Learning objectives are a deeper understanding of differential geometry concepts, as well as problems and solution strategies in their practical use.
    
    Previous knowledge: Differential geometry I

  • 19223811 Seminar
    Master Seminar Topology "L^2-Betti numbers" (N.N.)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-10-16)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of topology and group theory is required.

    Comments

    The Euler characteristic of finite CW-complexes is multiplicative under finite-sheeted coverings and it is homotopy invariant. These properties can be deduced from different descriptions:
    1. As the alternating sum of the numbers of cells, which are multiplicative but not homotopy invariant.
    2. As the alternating sum of Betti numbers, which are homotopy invariant but not multiplicative. The $n$-th Betti number of $X$ is the $\mathbb{Q}$-dimension of the homology $H_n(X;\mathbb{Q})$ with rational coefficients.
    3. As the alternating sum of $L^2$-Betti numbers, which enjoy the best features from both worlds: they are multiplicative and homotopy invariant. The $n$-th $L^2$-Betti number of $X$ is the von Neumann-dimension of the homology $H_n(X; \mathcal{N}\pi_1(X))$ with suitable coefficients.
    
    $L^2$-Betti numbers are meaningful topological invariants, as they obstruct the structures of mapping tori and $S^1$-actions. They also have applications to group theory by considering the $L^2$-Betti numbers of classifying spaces. Moreover, $L^2$-Betti numbers are related to famous open problems, such as the Hopf and Singer conjectures on the Euler characteristic of manifolds, and the Kaplansky conjecture on zero divisors in group rings.

    Detailed Information can be found on the Homepage of the seminar.

    Suggested reading

    This seminar will be an introduction to $L^2$-Betti numbers, following mostly
    the book by Holger Kammeyer.

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
    Location: SR A9
    

    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

  • 19247111 Seminar
    Ordinary Differential Equations (Marita Thomas)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Ordinary differential equations arise in many applications from physics, chemistry, biology or economics. This seminar extends the topics that were covered in the Analysis III course, e.g., eigenvalue problems and stability theory will be addressed. 

• Molecular Biology and Biochemistry I

  0260cA3.3
  • 21601a Lecture
    Biochemistry I - Fundamentals of Biochemistry (Helge Ewers, Florian Heyd, Markus Wahl)
    Schedule: Mi 12:00 - 14:00 Uhr; Vorbesprechung Di, 15.10.24, 12:00 - 14:00 Uhr (Class starts on: 2025-10-15)
    Location: Hs Kristallographie (Takustr. 6)
    

    Information for students

    Entspricht Molekularbiologie und Biochemie I für Bioinformatiker.

    Comments

    Qualifikationsziele:
    Die Studentinnen und Studenten kennen die Entstehung und molekulare Struktur der wichtigsten zellulären Makromoleküle und Stoffklassen sowie ihren biologischen Kontext. Der Schwerpunkt liegt auf einem chemischen Grundverständnis des molekularen Aufbaus von Biomolekülen.
    
    Inhalte:
    Chemische und zellbiologische Grundlagen, Struktur von DNA und RNA, Replikation und Transkription, Proteinbiosynthese, Regulation der Genexpression, gentechnologische Methoden, Aminosäuren und Peptide, Proteinstruktur und Proteinfaltung, Proteom, posttranslationale Modifikationen, Methoden der Proteinforschung, Enzyme, Kohlenhydrate, Lipide und Biomembranen, Einführung in den Stoffwechsel und die Stoffwechselregulation.
    
    Prof. Dr. H. Ewers: helge.ewers@fu-berlin.de
    Prof. Dr. F. Heyd: florian.heyd@fu-berlin.de
    Prof. Dr. M. Wahl: mwahl@zedat.fu-berlin.de
    

  • 21601b Practice seminar
    Tutorial for Biochemistry I - Fundamentals of Biochemistry (Helge Ewers, Florian Heyd, Markus Wahl)
    Schedule: (s. Lektionen, LV-Details) (Class starts on: 2025-10-21)
    Location: Ort nach Ansage je nach Übungsgruppe
    

    Additional information / Pre-requisites

    Die Übungen finden n.V. in kleineren Gruppen i.d.R. dienstags von 12:00 - 14:00 Uhr bzw. mittwochs von 10:00 - 12:00 Uhr Uhr statt. Die Verteilung findet im Rahmen der Vorbesprechung (s. 21601a) statt.

    Comments

    Qualifikationsziele: Die Studentinnen und Studenten kennen die Entstehung und molekulare Struktur der wichtigsten zellulären Makromoleküle und Stoffklassen sowie ihren biologischen Kontext. Der Schwerpunkt liegt auf einem chemischen Grundverständnis des molekularen Aufbaus von Biomolekülen. Inhalte: Chemische und zellbiologische Grundlagen, Struktur von DNA und RNA, Replikation und Transkription, Proteinbiosynthese, Regulation der Genexpression, gentechnologische Methoden, Aminosäuren und Peptide, Proteinstruktur und Proteinfaltung, Proteom, posttranslationale Modifikationen, Methoden der Proteinforschung, Enzyme, Kohlenhydrate, Lipide und Biomembranen, Einführung in den Stoffwechsel und die Stoffwechselregulation. Prof. Dr. H. Ewers: helge.ewers@fu-berlin.de Prof. Dr. F. Heyd: florian.heyd@fu-berlin.de Prof. Dr. M. Wahl: mwahl@zedat.fu-berlin.de

• Molecular Biology and Biochemistry II

  0260cA3.4
  • 21698a Lecture
    Molecular Biology and Biochemistry II (Francesca Bottanelli, Sutapa Chakrabarti, Helge Ewers, Lydia Herzel, Florian Heyd)
    Schedule: Do 10:00-12:00 Uhr (Class starts on: 2025-10-16)
    Location: Hörsaal/ Thielallee 67
    

    Information for students

    Qualifikationsziele: Die Studentinnen und Studenten haben ein Grundlagenverständnis in folgenden Bereichen: Zusammenwirken anatomischer, zellbiologischer und biochemische Prinzipien der Genexpression und des Energiestoffwechsels in Säugetieren, Regulation der Genexpression auf den Ebenen von Chromatinstruktur, Transkription, Prozessierung und Modifizierung in Säugetieren, Zell-Morphologie, -Mobilität und -Adhäsion in Organstrukturen von Säugetieren. Inhalte: Strukturprinzipien in Nuckleinsäuren und Proteinen, Chaperone und Ausbildung biologisch korrekter Protein Strukturen, Prinzipien der Struktur-Vorhersage, Genom-Komponenten und quantitative Zusammensetzung, Remodellierung von Chromatin zu transkribierbaren und nicht-transkribierbaren Konformationen, epigenetischer Histon-Code, CG-Inseln und DNA-Methylierung, modularer Aufbau der Promotoren, Protein: DNA-Wechelwirkungen und deren Strukturdomänen bei der qualitativen und quantitativen Steuerung der Transkription, snRNP und RNA-Prozessierung, Selbstspleißende Introns, RNA-Editierung, Kern-Cytoplasma, Cyotoplasma-Kern Transport, anatomische, zellbiologische und biochemische Prinzipien zur Gewinnung chemischer Reaktionsernergie, Protein-Abbau und Autophagie, Cytoskelett, Zell-Motilität und Zelladhäsion.
    

    UN Sustainable Development Goals (SDGs): 3, 14, 15

    Comments

    Prof. Bottanelli: bottanelli@zedat.fu-berlin.de Prof. Chakrabarti: sutapa.chakrabarti@fu-berlin.de Prof. Freund: christian.freund@fu-berlin.de Pro. Herzel: lydia.herzel@fu-berlin.de Prof. Heyd: florian.heyd@fu-berlin.de Dr. Preußner: marco.preussner@fu-berlin.de Prof. Wahl: mwahl@zedat.fu-berlin.de

  • 21698b Practice seminar
    Tutorial - Molecular Biology and Biochemistry II (Francesca Bottanelli, Sutapa Chakrabarti, Lydia Herzel, Florian Heyd)
    Schedule: Mi 13:00-15:00 Uhr (Class starts on: 2025-10-22)
    Location: Hörsaal/Thielallee 67 (Thielallee 67)
    

    Information for students

    Weitere Informationen unter:
    http://www.fu-berlin.de/sites/fimbb/lehre/
    

    UN Sustainable Development Goals (SDGs): 3, 14, 15

    Comments

    Prof. Bottanelli: bottanelli@zedat.fu-berlin.de Prof. Chakrabarti: sutapa.chakrabarti@fu-berlin.de Prof. Freund: christian.freund@fu-berlin.de Pro. Herzel: lydia.herzel@fu-berlin.de Prof. Heyd: florian.heyd@fu-berlin.de Dr. Preußner: marco.preussner@fu-berlin.de Prof. Wahl: mwahl@zedat.fu-berlin.de

• Genetics and Genome Research

  0260cA3.6
  • 23771a Lecture
    V Genetik und Genomforschung (V) (Katja Nowick)
    Schedule: siehe Terminserie (Class starts on: 2025-10-15)
    Location: siehe Terminserie
    

    Information for students

    UN Sustainable Development Goals (SDGs): 3, 5, 15

    Additional information / Pre-requisites

    Bitte melden Sie sich in CM nur für die Vorlesung an. Die Übung wird im Laufe des Semesters für Sie nachgetragen.
    
    Verbindliche Vorbesprechung am 1. Vorlesungstag (Mi, 15.10.2025; 13:00 Uhr)

    Comments

    Ein Überblick über den Aufbau der Lehrveranstaltung (d.h. Vorlesung und Übung) wird im Rahmen der ersten Vorlesung gegeben.
    
    Themen:
    Genregulation: Dogma der Molekularbiologie, Transkription, Translation, Transkriptionsfaktoren und deren Bindungsmotive
    Nicht-kodierende RNAs: Strukturen, Funktionen
    Genregulatorische Netzwerke: Komplexität der Genregulation, Analysemethoden
    Populationsgenetik: Vererbungsmuster und Erbkrankheiten, Mutation, Selektion, Hardy-Weinberg-Gleichgewicht, Neutrale Theory, Molekulare Uhr, Linkage Disequilibrium, Tests fuer positive Selektion in Populationen
    Phylogenetik: Bäume (rooted/unrooted), Neighbor joining, Maximum Parsimony, Maximum Likelihood, Tests für positive Selektion, Genomprojekte
    Genomtypen einer Zelle (nukleäres, mitochondriales und chloroplastisches Genom), Aufbau und Struktur des nukleären Genoms, Aufbau und Struktur von Chromosomen
    Funktion chromosomaler Strukturelemente (Replikationsursprung, Zentromer, Telomer), Steuerung des Zellzyklus, Modifikation von Histonen
    Karyogramm, Chromosomenanomalien
    Genfamilien und Prinzip der Homologie bei Genen, Next-Generation Sequencing
    Mono-allelische Expression
    Geschlechtsdetermination

  • 23771b Practice seminar
    Ü Genetik und Genomforschung (Ü) (Katja Nowick)
    Schedule: 28.01. - 18.02.2026; Mi; 13:00 - 16:00 (Class starts on: 2026-01-28)
    Location: Ehrenberg-Saal (R 126-132) (Königin-Luise-Str. 1 / 3)
    

    Information for students

    UN Sustainable Development Goals (SDGs): 3, 5, 15

    Additional information / Pre-requisites

    Bitte melden Sie sich in CM nur für die Vorlesung an. Die Übung wird im Laufe des Semesters für Sie nachgetragen.
    
    Wird am Ende des Semesters an 4 Terminen im Block durchgeführt.

    Comments

    Details werden im Rahmen der Vorbesprechung am 1. Vorlesungstag (Mi. 15.10.2025, 13:00 Uhr) bekannt gegeben.

• Neurobiology

  0260cA3.8
  • 23772a Lecture
    V Einführung in die Neurobiologie und Neuroinformatik für Studierende der Bioinformatik (Joachim Fuchs, Peter Robin Hiesinger, Ursula Koch, Gerit Linneweber, Eric Reifenstein, Max von Kleist, Mathias Wernet)
    Schedule: siehe Terminserie (Class starts on: 2025-10-16)
    Location: siehe Terminserie
    

    Information for students

    UN Sustainable Development Goals (SDGs): 3, 4, 5, 15

  • 23772b Internship
    P Neurobiologie für Studierende der Bioinformatik Kurs A (Edouard Joseph Babo, Joachim Fuchs, Peter Robin Hiesinger, Gerit Linneweber, Dagmar Malun, Mathias Wernet)
    Schedule: 3. Block: 05.01. - 02.02.2026; Mo; 08:00 - 12:00 (Class starts on: 2026-01-05)
    Location: Kursraum D/E (R 2/3) (Königin-Luise-Str. 1 / 3)
    

    Information for students

    UN Sustainable Development Goals (SDGs): 3, 4, 5, 15

    Additional information / Pre-requisites

    1 mal wöchentlich (Mo), insgesamt 5 Termine

  • 23772c Internship
    P Neurobiologie für Studierende der Bioinformatik Kurs B (Edouard Joseph Babo, Joachim Fuchs, Peter Robin Hiesinger, Gerit Linneweber, Dagmar Malun, Mathias Wernet)
    Schedule: 3. Block: 05.01. - 02.02.2026; Mo; 14:00 - 18:00 (Class starts on: 2026-01-05)
    Location: Kursraum D/E (R 2/3) (Königin-Luise-Str. 1 / 3)
    

    Information for students

    UN Sustainable Development Goals (SDGs): 3, 4, 5, 15

    Additional information / Pre-requisites

    1 mal wöchentlich (Mo), insgesamt 5 Termine

• Modules w/o courses in this semester

  150 Modules
  • Image Processing 0089cA1.1
  • Medical Image Processing 0089cA1.10
  • Model-driven Software Development 0089cA1.11
  • Pattern Recognition 0089cA1.12
  • Network-Based Information Systems 0089cA1.13
  • Project Management 0089cA1.14
  • Project Management (Specialization) 0089cA1.15
  • Computer Security 0089cA1.16
  • Semantic Business Process Management 0089cA1.17
  • Software Processes 0089cA1.18
  • Compiler Construction 0089cA1.19
  • Computer Graphics 0089cA1.2
  • Distributed Systems 0089cA1.20
  • XML Technology 0089cA1.21
  • Practices in Professional Software Development 0089cA1.22
  • Software Project: Applied Computer Science A 0089cA1.23
  • Software Project: Applied Computer Science B 0089cA1.24
  • Academic Work in Applied Computer Science A 0089cA1.25
  • Academic Work in Applied Computer Science B 0089cA1.26
  • Current research topics in Applied Computer Science 0089cA1.27
  • Special Aspects of Applied Computer Science 0089cA1.28
  • Advanced Topics in Data Management 0089cA1.29
  • Computer Vision 0089cA1.3
  • Special Aspects of Software Development 0089cA1.30
  • Selected Topics in Applied Computer Science 0089cA1.31
  • Database Technology 0089cA1.4
  • Empirical Evaluation in Computer Science 0089cA1.5
  • Fundamentals of Software Testing 0089cA1.7
  • Artificial Intelligence 0089cA1.9
  • Starting a Business in IT 0159cA2.2
  • Fundamentals of IT Project Management 0159cA2.6
  • Advanced Algorithms 0089cA2.1
  • Software Project: Theoretical Computer Science A 0089cA2.10
  • Software Project: Theoretical Computer Science B 0089cA2.11
  • Academic Work in Theoretical Computer Science A 0089cA2.12
  • Academic Work in Theoretical Computer Science B 0089cA2.13
  • Model Checking 0089cA2.2
  • Current Research Topics in Theoretical Computer Science 0089cA2.3
  • Computational Geometry 0089cA2.4
  • Selected Topics in Theoretical Computer Science 0089cA2.5
  • Advanced topics in Theoretical Computer Science 0089cA2.6
  • Special aspects of Theoretical Computer Science 0089cA2.7
  • Cryptography and Security in Distributed Systems 0089cA2.8
  • Semantics of Programming Languages 0089cA2.9
  • Operating Systems 0089cA3.1
  • Current Research Topics in Computer Systems 0089cA3.10
  • Special Aspects of Computer Systems 0089cA3.11
  • Selected Topics in Technical Computer Science 0089cA3.12
  • Microprocessor Lab 0089cA3.2
  • Mobile Communications 0089cA3.3
  • Robotics 0089cA3.4
  • Telematics 0089cA3.5
  • Software Project: Computer Systems A 0089cA3.6
  • Software Project: Computer Systems B 0089cA3.7
  • Academic Work in Computer Systems A 0089cA3.8
  • Academic Work in Computer Systems B 0089cA3.9
  • Computer-Oriented Mathematics II 0084dA1.7
  • Probability and Statistics I 0084dA1.8
  • Higher Analysis 0084dB2.1
  • Current Topics in Mathematics 0084dB2.10
  • Special topics in Applied Mathematics 0084dB2.13
  • Complex Analysis 0084dB2.3
  • Elementary Geometry 0084dB2.6
  • Geometry 0084dB2.7
  • Mathematical Project 0084dB2.9
  • Differential Equations I 0084dB3.1
  • Discrete Mathematics I 0084dB3.2
  • Algebra I 0084dB3.3
  • Topology I 0084dB3.6
  • Advanced and Applied Algorithms 0084dB3.7
  • Visualization 0084dB3.8.
  • Computer Algebra 0162bA1.2
  • Statistics Software (CoSta) 0162bA1.3
  • Introduction to Visualization 0162bA1.4
  • Panorama of Mathematics 0162bA1.5
  • Introductory Module: Differential Geometry II 0280bA1.2
  • Advanced Module: Differential Geometry III 0280bA1.3
  • Introductory Module: Algebra I 0280bA2.1
  • Introductory Module: Algebra II 0280bA2.2
  • Research Module: Algebra 0280bA2.4
  • Introductory Module: Discrete Mathematics I 0280bA3.1
  • Introductory Module: Discrete Geometry II 0280bA3.4
  • Advanced Module: Discrete Mathematics III 0280bA3.5
  • Research Module: Discrete Mathematics 0280bA3.7
  • Research Module: Discrete Geometry 0280bA3.8
  • Introductory Module: Topology I 0280bA4.1
  • Introductory Module: Visualization 0280bA4.3
  • Advanced Module: Topology III 0280bA4.4
  • Introductory Module: Numerical Analysis III 0280bA5.2
  • Advanced Module: Numerical Mathematics IV 0280bA5.3
  • Research Module: Numerical Mathematics 0280bA5.4
  • Introductory Module: Differential Equations I 0280bA6.1
  • Advanced Module: Differential Equations III 0280bA6.3
  • Research Module: Applied Analysis and Differential Equations 0280bA6.4
  • Complementary Module: Specific Aspects 0280bA7.3
  • Complementary Module: Specific Research Aspects 0280bA7.4
  • Complementary Module: Research Project 0280bA7.6
  • Introductory Module: Algebra I 0280cA1.1
  • Introductory Module: Dynamical Systems II 0280cA1.10
  • Introductory Module: Numerical Mathematics III 0280cA1.12
  • Introductory Module: Partial Differential Equations I 0280cA1.13
  • Introductory Module: Probability and Statistics III 0280cA1.16
  • Introductory Module: Topology I 0280cA1.17
  • Introductory Module: Number Theory II 0280cA1.19
  • Introductory Module: Algebra II 0280cA1.2
  • Introductory Module: Differential Geometry II 0280cA1.4
  • Introductory Module: Discrete Geometry II 0280cA1.6
  • Introductory Module: Dynamical Systems I 0280cA1.9
  • Advanced Module: Number Theory III 0280cA2.10
  • Advanced Module: Differential Geometry III 0280cA2.2
  • Advanced Module: Discrete Mathematics III 0280cA2.4
  • Advanced Module: Dynamical Systems III 0280cA2.5
  • Advanced Module: Partial Differential Equations III 0280cA2.7
  • Advanced Module: Probability and Statistics IV 0280cA2.8
  • 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 Discrete Geometry 0280cA3.3
  • Specialization Module: Master's Seminar on Discrete Mathematics 0280cA3.4
  • Specialization Module: Master’s Seminar on Dynamical Systems 0280cA3.5
  • Specialization Module: Master’s Seminar on Numerical Mathematics 0280cA3.6
  • Specialization Module: Master’s Seminar on Probability and Statistics 0280cA3.8
  • Complementary Module: Specific Research Aspects 0280cA4.10
  • Complementary Module: Research Project 0280cA4.11
  • Algorithmic Bioinformatics 0260cA1.5
  • Statistics I for Students of Life Sciences 0260cA2.5
  • Statistics II for Students of Life Sciences 0260cA2.6
  • General Chemistry 0260cA3.1
  • Molecular Biology and Biochemistry III 0260cA3.5
  • Medical Physiology 0260cA3.7
  • Biodiversity and Evolution 0262bB1.1
  • Medical Bioinformatics 0262bB1.2
  • Network Analysis 0262bB1.3
  • Physiology 0262bB1.4
  • Sequence Analysis 0262bB1.5
  • Structural Bioinformatics 0262bB1.6
  • Current Topics in Cell Physiology 0262bB2.1
  • Applied Sequence Analysis 0262bB2.2
  • Measurement and Analysis of Physiological Processes 0262bB2.3
  • Computational Systems Biology 0262bB2.4
  • Environmental Metagenomics 0262bB2.5
  • Current Topics in Medical Genomics 0262bB2.6
  • Current Topics in Structural Bioinformatics 0262bB2.7
  • Research Modules: Module A 0262bB3.1
  • Research Modules: Module B 0262bB3.2
  • Data Structures and Data Abstraction with Applications 0084dB2.8
  • Applied Modules: All Other Subjects 0089cD9.1
  • Elective Area (all other subjects) 0089cD9.2
  • Elective Area (all other subjects) 0089cD9.3
  • Elective Area (all other subjects) 0089cD9.4