Frontiers in Number Theory, Physics, and Geometry II

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent.More than ten years after a first meeting in 1989 between number theorists and physicists at the Centre de Physique des Houches, a second 2-week event focused on the broader interface of number theory, geometry, and physics.This book is the result of that exciting meeting, and collects, in 2 volumes, extended versions of the lecture courses, followed by shorter texts on special topics, of eminent mathematicians and physicists. The present volume has three parts: Conformal Field Theories, Discrete Groups, Renomalization. The companion volume is subtitled: On Random Matrices, Zeta Functions and Dynamical Systems (Springer, 3-540-23189-7). TOC:Part I: Conformal Field Theory. E. Frenkel: Lectures on the Langlands Program and Conformal Field Theory.- W. Nahm: Conformal Field Theory and Torsion Elements of the Bloch Group.- P. Cvitanovic: Tracks, Lie's, and Exceptional Magic.- P. Di Vecchia/A. Liccardo: Gauge Theories from D. Branes.- K. Wendland: On Superconformal Field Theories Associated to Very Attractive Quartics.- Part II: Discrete Groups. C. Soulé: An Introduction to Arithmetic Groups.- B. Pioline/A. Waldron: Automorphic Forms: A Physicist's Survey.- J. McKay/A. Sebbar: Replicable Functions: An Introduction.- D. Zagier: The Dilogarithm Function in Geometry and Number Theory.- H. Gangl/A.B.Goncharov/A. Levin: Multiple Logarithms, Algebraic Cycles and Trees.- M. Marcolli: Modular Curves, C-Algebras and Chaotic Cosmology.- G. Moore: Strings and Arithmetic.- Part III: Renormalization. A. Connes/M. Marcolli: Renormalization, The Riemann-Hilbert correspondence, and Motivic Galois Theory.- D. Kreimer: Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities.- S. Weinzierl: Algebraic Algorithms in Perturbative Calculations.