Explore a detailed mathematical lecture examining the relationship between Harish-Chandra bimodules with regular central characters and equivariant coherent sheaves on the Steinberg variety of connected reductive algebraic groups in positive characteristic. Learn how these bimodules implement translation functors for group representations and delve into the localization theory of Bezrukavnikov-Mirkovic-Rumynin. Discover how this theoretical framework establishes connections between coherent sheaves and perverse sheaves on the affine flag variety of the Langlands dual group, ultimately enabling the study of Lie algebra representations through constructible sheaves. Presented by Simon Riche from Université Clermont Auvergne at the Institut des Hautes Etudes Scientifiques (IHES), this advanced mathematical exploration provides fundamental insights into representation theory and algebraic geometry.