# Mehrdad Kalantar: A conjecture on type I locally compact groups

**Time: **
Wed 2021-12-01 17.00 - 18.00

**Location: **
Zoom, meeting ID: 694 6016 6420 (password required)

**Lecturer: **
Mehrdad Kalantar (University of Houston)

**Abstract:**

The notion of type I, hailing from the very origins of operator algebras and representation theory, can be seen as a rigorous way to define the class of groups for which unitary representations can be classified in any meaningful manner. By a celebrated result of Thoma, a discrete group is type I if and only if it is virtually abelian. In the non-discrete case, the current state of the art is not nearly as complete, despite numerous results ensuring that various important families of groups (e.g. every connected semisimple Lie group) are type I. What is completely lacking, in contrast to Thoma’s theorem, is a definite structural consequence of type I. This talk is around the following conjecture: Every second countable locally compact group of type I admits a cocompact amenable subgroup. We motivate the conjecture, provide some supporting evidence for it, and prove it for type I hyperbolic locally compact groups admitting a cocompact lattice.

This is joint work with Pierre-Emmanuel Caprace and Nicolas Monod.

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