## ULethbridge Number Theory and Combinatorics Seminar: Mathieu Dutour

- Date: 11/28/2022
- Time: 12:00

University of Lethbridge

Theta-finite pro-Hermitian vector bundles from loop groups elements [video]

In the finite-dimensional situation, Lie's third theorem provides a correspondence between Lie groups and Lie algebras. Going from the latter to the former is the more complicated construction, requiring a suitable representation, and taking exponentials of the endomorphisms induced by elements of the group.

As shown by Garland, this construction can be adapted for some Kac-Moody algebras, obtained as (central extensions of) loop algebras. The resulting group is called a loop group. One also obtains a relevant infinite-rank Chevalley lattice, endowed with a metric. Recent work by Bost and Charles provide a natural setting, that of pro-Hermitian vector bundles and theta invariants, in which to study these objects related to loop groups. More precisely, we will see in this talk how to define theta-finite pro-Hermitian vector bundles from elements in a loop group. Similar constructions are expected, in the future, to be useful to study loop Eisenstein series for number fields.

This is joint work with Manish M. Patnaik.

**Location**: M1040

**Time: **12pm Mountain/ 11am Pacific

Live access links are posted here and on https://researchseminars.org/seminar/NTC. A recording of this event is available on mathtube.org.