Department of Mathematics - Seminar on Pure Mathematics - Partitions and Compactifications of
Loop Arithmetic Quotients

The notion of semi-stability and ‘canonical’ filtrations for Euclidean lattices grew out of the work of Harder and Narasimhan on vector bundles on curves. It has been used by several authors to give a partition of arithmetic quotients of reductive groups. I will try to explain how this picture generalizes to infinite-dimensional loop groups and sketch how it can be used to study a version of Borel-Serre compactifications in this context.

Joint work with Punya Satpathy.