**Contemporary Mathematics** 2011; 277 pp; softcover Volume: 543 ISBN-10: 0-8218-4985-9 ISBN-13: 978-0-8218-4985-9 List Price: US$104 Member Price: US$83.20 Order Code: CONM/543
| This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Representations of Reductive, \(p\)-adic Groups, which was held on January 16, 2010, in San Francisco, California. One of the original guiding philosophies of harmonic analysis on \(p\)-adic groups was Harish-Chandra's Lefschetz principle, which suggested a strong analogy with real groups. From this beginning, the subject has developed a surprising variety of tools and applications. To mention just a few, Moy-Prasad's development of Bruhat-Tits theory relates analysis to group actions on locally finite polysimplicial complexes; the Aubert-Baum-Plymen conjecture relates the local Langlands conjecture to the Baum-Connes conjecture via a geometric description of the Bernstein spectrum; the \(p\)-adic analogues of classical symmetric spaces play an essential role in classifying representations; and character sheaves, originally developed by Lusztig in the context of finite groups of Lie type, also have connections to characters of \(p\)-adic groups. The papers in this volume present both expository and research articles on these and related topics, presenting a broad picture of the current state of the art in \(p\)-adic harmonic analysis. The concepts are liberally illustrated with examples, usually appropriate for an upper-level graduate student in representation theory or number theory. The concrete case of the two-by-two special linear group is a constant touchstone. Readership Graduate students and research mathematicians interested in representations of \(p\)-adic groups. |