19202001
Lecture
WiSe 22/23: Discrete Geometrie I
Christian Haase
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.
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Suggested reading
- G.M. Ziegler "Lectures in Polytopes"
- J. Matousek "Lectures on Discrete Geometry"
- Further literature will be announced in class.
32 Class schedule
Additional appointments
Mon, 2023-02-27 12:00 - 14:00Diskrete Geometrie I (Klausur 1)
Mon, 2023-03-27 12:00 - 14:00
Diskrete Geometrie I (Klausur 2)
Regular appointments
Tue, 2022-10-18 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-10-25 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-11-01 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-11-08 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-11-15 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-11-22 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-11-29 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-12-06 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2022-12-13 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2023-01-03 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2023-01-10 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2023-01-17 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2023-01-24 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2023-01-31 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2023-02-07 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Tue, 2023-02-14 10:00 - 12:00
Diskrete Geometrie I (Serientermin 1)
Wed, 2022-10-19 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-10-26 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-11-02 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-11-09 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-11-16 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-11-23 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-11-30 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-12-07 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2022-12-14 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2023-01-04 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2023-01-11 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2023-01-18 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2023-01-25 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2023-02-01 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2023-02-08 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)
Wed, 2023-02-15 10:00 - 12:00
Diskrete Geometrie I (Serientermin 2)