# Grzegorz Jagiella: Definable topological dynamics and o-minimality

Set Theory and Topology seminar (BGU)

Time: Tuesday, ​December 15, 12:15-13:40.
Place: Seminar room -101, Math building 58.
Speaker: Grzegorz Jagiella (Haifa University).
Title: Definable topological dynamics and o-minimality
Abstract: Fix a model $M$. For an $M$-definable group $G$ acting definably and transitively on a definable set $X$, we can consider the induced action on the space $S_X(M)$ of types on $X$. This is an action by homeomorphisms (where $S_X(M)$ is equipped with the standard Stone space topology), making the pair $(G(M),S_X(M))$ a $G(M)$-flow in the sense of classic topological dynamics. I will discuss how various notions of toplogical dynamics are interpreted in the sense of model theory. I will then present the results on the universal definable flows of groups definable in an o-minimal setting (e.g. definable real Lie groups).