A convolution morphism is the geometric analogue of the convolution of functions in a Hecke algebra. The properties of fibres of convolution morphisms are used in a variety of ways in the geometric Langlands programme and in the study of Schubert varieties. I will explain a very general result about cellular pavings of fibres of convolution morphisms in the setting of partial affine flag varieties, as well as applications related to the very purity and parity vanishing of cohomology of Schubert varieties over finite fields, structure constants for parahoric Hecke algebras, and the (motivic) geometric Satake equivalence.
The talk is based on this arXiv paper.
This video was part of the Southeastern Lie Theory Workshop XIV on quantum structure in Lie theory.
