Mathematics Colloquium

Professor Mehrdad Kalantar
On type I hyperbolic locally compact groups


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. 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.



*The Math Colloquium will be available live via Zoom at and recordings of the sessions will be available at usually within a couple hours of the colloquium finishing.

Event Date: 
March 2, 2023 - 3:30pm
213 MLH and Online (see URL)
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