Polish groups and automatic continuity (exposé dans le cadre des rencontres Franco-Colombiennes).

par Alex Berenstein (Universidad de los Andes)

jeudi 14 déc. 2017, 09:45 → 10:45 Europe/Paris

4ème étage salle 435 (ENS Lyon Site Monod)

In this talk I will give an introduction to Polish groups and automatic continuity. We say that a topological group is Polish if it is separable and completely metrizable. We say a Polish group has the automatic continuity property if any algebraic morphism to any separable topological group is continuous.
In joint work with I. Ben Yaacov (ICJ) and J. Melleray (ICJ) we studied these concepts for some groups of isometries and gave a criteria for automatic continuity. I will talk about these criteria and then I will discuss ongoing work with Rafael Zamora (Ph.D. Paris 6) on the group of isometries of some metric structures called randomizations.