Prof. Giulia Codenotti
Arnimallee 2, room 105 (Office hours: Wed 15:30-16:30 or by appointment)

Sophie Rehberg
Arnimallee 2, room 103 (office hours: TBA)

Schedule

Lectures Tuesday 10-12 T9/SR 006 Seminarraum
Wednesday 10-12 Königin-Luise-Str. 24 / 26, SR 006
Exercises Friday 14-16 Arnimallee 6 SR 032

Exams

The final exam will take place on Tuesday, February 20th 2024 at 10:00. The date of the make up exam will be announced during the semester.

Contents

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!

  • Regular polytopes, centrally symmetric polytopes
  • Extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
  • Combinatorial optimization and 0/1-polytopes

Prerequisites

A good grasp of linear algebra is all that is necessary. Knowledge of combinatorics or geometry can be helpful.

Formalities

Please note that passing the exam AND obtaining 50% or more of the points on the exercise sheets AND actively participating in the exercise sessions are required to complete the course.
Please check out the organization sheet for all the details!