19202001 Lecture

WiSe 20/21: Discrete Geometrie I

Matthias Beck

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.

30 Class schedule

Regular appointments

Tue, 2020-11-03 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2020-11-10 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2020-11-17 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2020-11-24 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2020-12-01 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2020-12-08 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2020-12-15 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-01-05 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-01-12 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-01-19 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-01-26 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-02-02 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-02-09 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-02-16 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Tue, 2021-02-23 08:00 - 10:00
Diskrete Geometrie I (Serientermin 1)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2020-11-06 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2020-11-13 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2020-11-20 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2020-11-27 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2020-12-04 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2020-12-11 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2020-12-18 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-01-08 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-01-15 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-01-22 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-01-29 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-02-05 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-02-12 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-02-19 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)

Fri, 2021-02-26 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)

Lecturers:
Prof. Matthias Beck

Location:
T9/Gr. Hörsaal (Takustr. 9)