James Freitag : Highly transitive group actions

Posted by James Freitag , part of the Logic Seminar.

At

Feb. 4, 2020, 3 p.m.

In

427 SEO

Abstract

It is a classical result (combining results of Tits and Hall) that there is no sharply 4-transitive action of a group on an infinite set. For algebraic groups acting on (infinite) varieties, there is no 4-transitive group action. Things get more interesting when we loosen the requirements slightly and merely demand that the action has a "large" orbit for a suitable notion of large. In this talk we will discuss some conjectures in this area and the current prospects for solving them. We will also talk about the connection between conjectures in this area and some notions from geometric stability theory.