K-Motives and Koszul Duality

Abstract: Koszul duality, as conceived by Beilinson-Ginzburg-Soergel, describes a remarkable symmetry in the representation theory of Langlands dual reductive groups. Geometrically, Koszul duality can be stated as an equivalence of categories of mixed (motivic) sheaves on flag varieties. In this talk, I will argue that there should be an an 'ungraded' version of Koszul duality between monodromic constructible sheaves and equivariant $K$-motives on flag varieties. For this, I will explain what $K$-motives are and present preliminary results.

mathematical physicsalgebraic geometryrepresentation theory

Audience: researchers in the topic

Geometric Representation Theory conference

Series comments: Originally planned as a twinned conference held simultaneously at the Max Planck Institute in Bonn, Germany and the Perimeter Institute in Waterloo, Canada. The concept was motivated by the desire to reduce the environmental impact of conference travels. In order to view the talks, register at the website: www.mpim-bonn.mpg.de/grt2020 . The talks from previous days can be be viewed at pirsa.org/C20030 ; slides from the talks are posted here: www.dropbox.com/sh/cjzqbqn7ql8zcjv/AAANB82Hh4t5XDc5RPcZzW0Aa?dl=0