ESI Lectures in Mathematics and Physics 2011; 280 pp; softcover Volume: 8 ISBN10: 3037190086 ISBN13: 9783037190081 List Price: US$78 Member Price: US$62.40 Order Code: EMSESILEC/8
 This collection of expository articles grew out of the workshop "Number Theory and Physics" held in March 2009 at The Erwin Schrödinger International Institute for Mathematical Physics, Vienna. The common theme of the articles is the influence of ideas from noncommutative geometry (NCG) on subjects ranging from number theory to Lie algebras, index theory, and mathematical physics. Matilde Marcolli's article gives a survey of relevant aspects of NCG in number theory, building on an introduction to motives for beginners by Jorge Plazas and Sujatha Ramdorai. A mildly unconventional view of index theory, from the viewpoint of NCG, is described in the article by Alan Carey, John Phillips, and Adam Rennie. As developed by Alain Connes and Dirk Kreimer, NCG also provides insight into novel algebraic structures underlying many analytic aspects of quantum field theory. Dominique Manchon's article on preLie algebras fits into this developing research area. This interplay of algebraic and analytic techniques also appears in the articles by Christoph Bergbauer, who introduces renormalization theory and Feynman diagram methods, and Sylvie Paycha, who focuses on relations between renormalization and zeta function techniques. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in number theory and physics. Table of Contents  C. Bergbauer  Notes on Feynman integrals and renormalization
 S. Ramdorai, J. Plazas, and M. Marcolli  Introduction to motives. With an appendix by Matilde Marcolli
 D. Manchon  A short survey on preLie algebras
 S. Paycha  Divergent multiple sums and integrals with constraints: A comparative study
 A. Carey, J. Phillips, and A. Rennie  Spectral triples: Examples and index theory
 List of contributors
 Index
