Harmonic analysis, the trace formula, and Shimura varieties : proceedings of the Clay Mathematics Institute, 2003 Summer School, the Fields Institute, Toronto, Canada, June 2-27, 2003

In these proceedings from the school held in June 2003, the presenters give introductions to the subject of automorphic forms that have come to be called the Langlands program. Although the reciprocity laws proposed by Langlands are still largely unproved, the program ties arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representation. The presenters' topics include an introduction to the trace formula and Shimura varieties (including those with bad reductions of parahoric type), linear algebraic groups, harmonic analysis on reductive p-adic groups and Lie algebras, homogeneity for reductive p-adic groups, compactifications and cohomology of modular varieties, the fundamental lemma, and the generalized Ramanujan conjectures. Annotation 2006 Book News, Inc., Portland, OR (booknews.com) Cover......Page 1 Contents......Page 6 Preface......Page 8 An Introduction to the Trace Formula......Page 14 Introduction to Shimura Varieties......Page 278 Linear Algebraic Groups......Page 392 Harmonic Analysis on Reductive p-adic Groups and Lie Algebras......Page 406 Homogeneity for Reductive p-adic Groups: An Introduction......Page 536 Compactifications and Cohomology of Modular Varieties......Page 564 Introduction to Shimura Varieties with Bad Reduction of Parahoric Type......Page 596 A Statement of the Fundamental Lemma......Page 656 Notes on the Generalized Ramanujan Conjectures......Page 706 List of Participants......Page 700 Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.