This is a learning seminar on Geometric representation theory organized by Katia Bogdanova, Ivan Losev and Sam Raskin. This semester we concentrate on integral versions of classical equivalence in Geometric Representation theory/ Langlands program: the geometric Satake equivalence due to Mirkovic and Vilonen, see here and, if time permits, the integral version of the Arkipov-Bezrukavnikov equivalence due to Dhillon and Taylor, see here.