# Mini-course by Prof. Ron Aharoni "Choice functions"

At the invitation of the Laboratory of Combinatorial and Geometric Structures and the PhysTech School of Applied Mathematics and Computer Science, Ron Aharoni will visit the Moscow Institute of Physics and Technology on September 14-20.

Ron Aharoni will give 3 lectures on September 16-18 from 13.55 to 15.20 in the lecture auditorium on the 4th floor of the Arctic building. In this mini-course, he will introduce us to the multi-colored analogues of some of the well-known combinatorial theorems, as well as interesting open questions in the field and the topological and combinatorial basics necessary to obtain these results.

"I will start with some basic facts about topology, and then speak about its application to choice functions.

There are two types of choice functions, one in which the domain is demanded to be large (the classical case being Hall's theorem, where all men are to be married, and the condition is on how many women does any subset of the men connected to) and one in which the range is required to be large (a classical case is the Lov'asz-Barany colorful Caratheodory theorem, in which the range should contain a given vector in its convex hull, and the condition is that every set contains the vector in its convex hull). Results in the first are usually Hall-like - if every k sets contain "many" elements, then there exists a choice function as required. Results in the second type are usually of the form "if there are many sets, each being large, then...". I will discuss the question of whether there are Hall-like theorems also for the second family."

Everyone is invited to attend the lecture course. The language of the lectures is English. The course is aimed at master and graduate students, as well as researchers in the field of combinatorics.