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Explore the intricate world of geometric representation theory in this 53-minute lecture by Laura Rider from the Hausdorff Center for Mathematics. Delve into the two categorical realizations of the affine Hecke algebra: constructible sheaves on the affine flag variety and coherent sheaves on the Langlands dual Steinberg variety. Discover the fundamental problem of relating these two categories through a category equivalence, a challenge solved by Bezrukavnikov in characteristic 0 about a decade ago. Learn about the ongoing efforts to solve this problem in the modular case, as Rider discusses her joint work with R. Bezrukavnikov and S. Riche, focusing on modular perverse sheaves on the affine flag variety as a crucial first step towards this goal.
