Learning Seminar on Geometric Representation Theory

We briefly review combinatorics and algebraic representation of reductive groups: root systems, Weyl groups and (extended) affine Weyl groups, weight spaces, and classification of irreducible representations in terms of highest weights. We define the Langlands dual group. We review p-adic groups and their (smooth) representations, including: Hecke algebras attached to compact open subgroups, relation between representations and Hecke modules, classical Satake isomorphism and its proof (sketch). If time permits, we discuss the unramified local Langlands correspondence.