Motives in Geometric Representation Theory III

Abstract: Recent constructions in motivic homotopy theory offer exciting new applications in geometric representation theory. For example, they allow to consider mixed perverse sheaves (a graded version of perverse sheaves) with integral coefficients or K-motives (a K-theoretic analogue of constructible sheaves).

In this lecture series, we will explain how to work with motives in practice. We focus on motivic cohomology, the motivic six functor formalism, Tate motives, and weight structures. We will then explain the notion of stratified mixed Tate motives which, when specialized to (affine/partial) flag varieties, yields a geometric perspective on Koszul duality. Lastly, we will introduce results and conjectures relating K-motives and the geometric Langlands program.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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