**EMS ESI Lectures in Mathematics and Physics**

Volume: 8;
2011;
280 pp;
Softcover

MSC: Primary 58; 11; 47; 81; 17; 16; 18; 46; 19;
**Print ISBN: 978-3-03719-008-1
Product Code: EMSESILEC/8**

List Price: $78.00

Individual Member Price: $62.40

# Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory

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*Alan Carey*

A publication of the European Mathematical Society

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 pre-Lie 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.

#### Table of Contents

# Table of Contents

## Noncommutative Geometry and Physics: Renormalisation, Motives, Index Theory

#### Readership

Graduate students and research mathematicians interested in number theory and physics.