Oberseminar p-adic groups and Bruhat-Tits buildings 1.Clemens Nollau, Lou-Jean Cobigo-Bihavan: Linear algebraic groups - groups over algebraically closed fields, Borel and parabolic subgroups - roots and highest weight theory - arbitrary fields, Galois actions, splitness and Galois cohomology Literature: - Borel: Linear algebraic groups - Mumford/Kirwan: Geometric Invariant Theory - Serre: Galois Cohomologie 2. Felix Röhrle: Local and global fields - local fields, extensions, Haar measures, zeta intgerals, Tate’s thesis - global fields, adeles and ideles - linear groups over local fields and adeles, integral points, Tamagawa measure Literature: - Deitmar: Automorphic forms - Weil: Basic Number Theory - Weil: Adeles and algebraic groups 3. Parisa Ebrahimian: Bruhat-Tits buildings - abstract definition of a building - spherical and affine buildings of p-adic groups - split tori and apartments Literature: - Serre: Trees - Bourbaki: Lie Groups and Lie Algebras: Chapters 4–6 - Brown: Buildings - Witte-Morris: Introduction to Bruhat-Tits Buildings - Tits: Reductive groups over local fields 4. Representations of p-adic groups - parabolically induced representations and the Jacquet functor - supercuspidal representations Literature: - Cartier; Representations of p-adic groups: A Survey 5. Giacomo Gavelli: The trace formula local and global - invariant distributions, Harish-Chandra characters - trace formula local: graphs/buildings and Riemann surfaces - trace formula global = limit of S-locals - comparison of traces, Jacquet-Langlands correspondence Literature: - Deitmar/Echterhoff: Priciples of Harmonic Analysis - Gelbart/Jacquet: Forms of GL(2) from the analytic point of view