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 IRMA Lectures in Mathematics and Theoretical Physics 2006; 275 pp; softcover Volume: 10 ISBN-10: 3-03719-028-0 ISBN-13: 978-3-03719-028-9 List Price: US$48 Member Price: US$38.40 Order Code: EMSILMTP/10 There is a rich and historical relationship between theoretical physics and number theory. This volume presents a selection of problems which are currently in full development and inspire a lot of research. Each of the seven contributions starts with an introductory survey which makes it possible even for non-specialists to understand the results and to gain an idea of the great variety of subjects and techniques used. Topics covered are: phase locking in oscillating systems, crystallography, Hopf algebras and renormalisation theory, Zeta-function and random matrices, Kloosterman sums and the local Langlands correspondence. Intended for research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of recent developments in an exciting subject crossing several disciplines. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in number theory and mathematical physics. Table of Contents M. Planat -- The phase of oscillations and prime numbers: classical and quantum J.-L. Verger-Gaugry -- On self-similar finitely generated uniformly discrete (SFU-)sets and sphere packings J.-P. Gazeau, Z. Masáková, and E. Pelantová -- Nested quasicrystalline discretisations of the line C. Bergbauer and D. Kreimer -- Hopf algebras in renormalization theory: locality and Dyson-Schwinger equations from Hochschild cohomology E. Royer -- Fonction $$\zeta$$ et matrices aléatoires P. Michel -- Some recent applications of Kloostermania A. Mézard -- Introduction à la correspondance de Langlands locale