## Vorlesungsverzeichnis

19202001 Vorlesung

# WiSe 14/15: Diskrete Geometrie I

## Raman Sanyal

### Hinweise für Studierende

Klausurtermin am 11.02.2015, 10-12 Uhr im Raum 001 A3/Hörsaal

### Zusätzl. Angaben / Voraussetzungen

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

### Kommentar

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,
• Szemeredi--Trotter
• 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. Schließen

### Literaturhinweise

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

### 32 Termine

Zusätzliche Termine

Do, 16.04.2015 12:00 - 14:00
Nachklausur

Räume:
Hs 001/A3 Hörsaal (Arnimallee 3-5)

Regelmäßige Termine der Lehrveranstaltung

Di, 14.10.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 21.10.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 28.10.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 04.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 11.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 18.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 25.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 02.12.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 09.12.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 16.12.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 06.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 13.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 20.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 27.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 03.02.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Di, 10.02.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 15.10.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 22.10.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 29.10.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 05.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 12.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 19.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 26.11.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 03.12.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 10.12.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 17.12.2014 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 07.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 14.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 21.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 28.01.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 04.02.2015 10:00 - 12:00

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)

Mi, 11.02.2015 10:00 - 12:00
Klausur

Dozenten:
Prof. Dr. Raman Sanyal

Räume:
SR 007/008/A6 Seminarraum (Arnimallee 6)