Course description
MAS 581 C: Combinatorial Convexity
The course will cover several topics in combinatorial convexity, where theorems of Caratheodory, Helly, Radon, and Tverberg are the typical and classical results. We plan to investigate weak epsilons-nets, halving lines and planes, the (p,q)-problem and its solution, extensions to lattice convex sets, and colourful versions of theorems of Helly, Caratheodory, Radon, Tverberg, and the like. The methods here use tools from linear algebra, combinatorics, topology, geometry, probability theory, and geometry of numbers.
Lectures
This is a 1-credit intensive course given by Professor Imre Bárány. There will be daily lectures starting Monday 04/29 to Friday 05/03. A final written exam will be given on Saturday 05/04.
Imre Bárány
Imre Bárány is a member of the Alfréd
Rényi Institute of Mathematics in Budapest and of the
University College of London. His main research interests are in
combinatorics and discrete geometry. Among his main contributions,
he gave a surprisingly simple alternative proof of Lovász
theorem on the chromatic number of Kneser graphs, he solved a
problem of Sylvester on the probability of random point sets in
convex position, he gave colored versions of Caratheodoy and Helly
theorems and proved a central limit theorem on random points in
convex bodies. He received the Erdös prize of the Hungarian
Academy of Sciences in 1982, was invited speaker in the ICM 2002
held in Beijing and he is in the Editorial Board of several
journals, including Combinatorica, Mathematika, and the Online
Journal of Analytic Combinatorics.