Combinatorial and Discrete Geometry course information

Code: BMETE94MM02 (3/1/0/V/5);
Semester: 2025/26/1;
Language: English;
Instructor: Dr. Péter Vrana (E0 course)

Grading

The grade is determined based on an oral exam. Please find the list of topics here.

Schedule

Wednesdays 12:15–13:45 and 14:00–15:30

Planned topics: (to be updated as the semester progresses)

  • September 10, Affine subspaces and convex sets
  • September 17, Polytopes and polyhedral sets
  • September 24, Algebra of convex sets, valuations, Euler characteristic
  • October 1, Face structure
  • October 8, Graphs of polytopes
  • October 15, Incidence problems
  • October 22, Arrangements
  • October 29, Ramsey-type problems
  • November 5, Antipodal sets
  • November 12, Hadwiger number
  • November 19, no class, Students' Scientific Association Conference (TDK)
  • November 26, Hadwiger number of star-convex sets
  • December 3, Borsuk problem
  • December 10, Simplicial complexes, Brouwer fixed point theorem

Lectures

The latest version of the lecture notes may be found here. (Updated: December 10)

Consultation

By appointment.

Recommended literature

  1. The lecture notes for the convex geometry course contain additional details on some of the topics (including many proofs omitted in this course).
  2. Alexander Barvinok: A Course in Convexity, Graduate Studies in Mathematics 54, AMS, Providence RI, USA, 2002.
  3. Jiří Matoušek: Lectures on Discrete Geometry, Graduate Texts in Mathematics 212, Springer-Verlag, New York NY, USA, 2002.
  4. Günter M. Ziegler: Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer-Verlag, New York NY, USA, 1998.
  5. Jiří Matoušek: Using the Borsuk–Ulam Theorem, Lectures on Topological Methods in Combinatorics and Geometry, Springer-Verlag, New York NY, USA, 2003.
  6. Szabó László: Konvex geometria, egyetemi jegyzet, ELTE TTK, Budapest, 1996. (in Hungarian)
  7. G. Horváth Ákos, Lángi Zsolt: Kombinatorikus geometria, egyetemi jegyzet, Polygon, Szeged, 2012. (in Hungarian)