Modular representations and perverse sheaves on affine flag varieties

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I will give an overview of a joint project with Simon Riche and Laura Rider and another one with Dima Arinkin aimed at a modular version of the equivalence between two geometric realization of the affine Hecke algebra and derived Satake equivalence respectively. As a byproduct we obtain a proof of the Finkelberg-Mirkovic conjecture and a possible approach to understanding cohomology of higher Frobenius kernels with coefficients in a G-module.