Open Problems in Discrete Geometry

Lectures are on Monday and Wednesday 9:15-10:30 in Mondi 2
Recitations are Monday 11:45-12:35 in Mondi 2
Instructor: Herbert Edelsbrunner and Arseniy Akopyan
Teaching Assistant: Anton Nikitenko

Announcements

Schedule

Date Lecture Topic Notes Assignments
February 29 Mon 1 Bang's conjecture and covering problems  
March 02 Wed 1 continued
 
March 07 Mon 2 Intrinsic volumes. The Crofton formula
 
March 09 Wed 2 continued
March 14 Mon 3 Kneser–Poulsen problems and sphere packing
 
March 16 Wed 3 continued
 
April 4 Mon 4 Stochastic geometry
April 6 Wed 4 continued
 
April 11 Mon 5 Borsuk and distance problems
 
April 13 Wed 5 continued
 
April 18 Mon 6 Billiards
April 20 Wed 6 continued and finish

List of Open Problems for Presentations

0. Your favorite discrete geometry open problem.
1. The Danzer problem on large empty convex body. Paper of O. Solan, Y. Solomon and B. Weiss.
2. Fire control problem. See Alberto Bressan publication list.
3. Illumination of boundary of convex body. See chapter 3 in K. Bezdek book.
4. Voronoi's conjecture. See section 4.3 in book Brass, Peter, William Moser, and Janos Pach. Research problems in discrete geometry. Springer Science & Business Media, 2006.
5. Universal covers? Lebesgue's Universal Covering Problem and similar questions.
6. Mahler conjecture. See wikipedia.org/Mahler_volume.
7. Einstein problem. See wikipedia.org/Einstein_problem.


Herbert Edelsbrunner (edels@ist.ac.at) February 2016