Speaker: Robert Simon (London School of Economics and Political Science)
Title:  Proper graph colouring, optimization, and paradoxical decompositions

Date: Tuesday, April 15^th , 2025
Time: 10:30 am- 11:30am
Location: 509/511 Lake Hall

Abstract: We show that there is an infinite graph of finite degree defined by a Borel equivalence relation on a probability space such that it can be coloured properly with 17 colours but only in ways that induce paradoxical decompositions. We show that there are problems of optimization such that every epsilon-optimal solution for small enough positive epsilon induces a paradoxical decomposition.

Biography:    Professor Simon an Associate Professor in the Department of Mathematics. Before this, he got an undergraduate degree in Political Science at Reed College, an M.Sc. in Mathematics at Ohio State University, a Ph.D. in Mathematics at Bielefeld (Germany) and an Habilitation in Mathematics at Goettingen (Germany). He did postdoctoral work at the Hebrew University.
Research wise, he is part of the Analysis group. Much of his past work has been with various mathematical problems related to game theory. Today his main efforts concern the Banach Tarski Paradox, the existence of orbits in dynamical systems, and topological structures. He is interested in any good problem of mathematics and is willing to discuss any topic.