discipline

MSC in Mathematics, Pure Mathematics, Elective Course

subject

Combinatorial Convexity

lecturers

Dr. Károly Bezdek (professor),

Dr. Károly Böröczky (professor),

Dr. Károly Böröczki Jr. (associate professor),

Dr. Gábor Kertész (assistant professor).

credits

2

period

2nd semester

curriculum

Euler-Poincaré theorem, Dehn-Sommerwill equations. Cyclic polytopes. Upper bound theorem, Gale-transform. Random polytopes for Gauss-distribution, Koebe’s circle theorem about planar graphs, Steinitz’s theorem, edge graphs of polytopes (Balinski’s theorem). Universality theorem. Convex hull algorithms. Ellipsoid algorithm. Polynomial algorithm for counting lattice points.

literature

B. Grünbaum: Convex polytopes, 2nd edition, Springer-Verlag, 2003.

form of tuition

Two hours of lecture per week.

mode of assessment

oral exam