Instructional Conference on Representation Theory and Arithmetic Notes Taken by Mike Woodbury
نویسندگان
چکیده
Goal of Conference 2 1. Matt Emerton: Classical Modular Forms to Automorphic Forms 2 1.1. The Growth Condition 3 1.2. Passage to Representation Theory 4 2. David Nadler: Real Lie Groups 5 2.1. Basic Notions 5 2.2. Examples 5 2.3. Classification 6 2.4. Useful Decompositions 7 3. Jacob Lurie: Lie Theory and Algebraic Groups 8 3.1. Classification 9 4. Jacob Lurie: Representations of algebraic groups 10 5. Matt Emerton 13 6. Florian Herzig: Representation theory of p-adic groups 16 7. David Nadler: Hecke algebras 16 7.1. Distributions: from groups to algebras 16 8. Frank Calegari: Representations of GL2(Fq) 17 8.1. Whittaker models and the Weil representation: Cuspidal representations 18 8.2. Final thoughts 20 9. Frank Calegari: class field theory 20 9.1. Frobenius elements 20 9.2. Artin map 21 9.3. Adelic language 22 10. Matt Emerton: Automorphic forms and representations 24 10.1. Groups over Q 25 10.2. Authomorphic forms 26 11. Frank Calegari: Problem session 27 11.1. Proof of Theorem 52 27 12. Matt Emerton: Automorphic forms 28 12.1. Definition of automorphic forms 28 12.2. Eisenstein series 29 12.3. Cusp forms 30 12.4. Ramanujan’s conjecture 30 12.5. Hecke operators 31
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