Lectures of the Les Houches School
Frontiers in Number Theory, Physics and Geometry

volume I -- volume II

Préface en français aux deux volumes
Table of contents of volume I
You can order this book online from Springer site.

Frontiers in Number Theory, Physics and Geometry Volume 1: On random matrices, zeta functions and dynamical systems

Preface

Part I : Random matrices: from Physics to Number theory

Quantum and Arithmetic Chaos E. Bogomolny
Notes on L-functions and Random Matrix Theory J. Brian Conrey
Energy level statistics, lattice point problems, and almost modular functions Jens Marklof
Arithmetic quantum chaos of Maass waveforms H. Then
Large N expansion for normal and complex matrix ensembles P. Wiegmann, A. Zabrodin
Symmetries Arising from Free Probability Theory Dan Voiculescu
Universality and Randomness for the Graphs and Metric Spaces A. M. Vershik

Part II: Zeta functions

From Physics to Number theory via Noncommutative Geometry Alain Connes, Matilde Marcolli
More Zeta Functions for the Riemann Zeros André Voros
Hilbert Spaces of Entire Functions and Dirichlet L-Functions Jeffrey C. Lagarias
Dynamical Zeta functions and closed orbits for geodesic and hyperbolic flows Mark Pollicott

Part III: Dynamical Systems: Beyond Diophantus and Brjuno

Continued Fraction Algorithms for Interval Exchange Maps: an Introduction Jean-Christophe Yoccoz
Flat surfaces Anton Zorich
Brjuno numbers and dynamical systems Guido Gentile
Some Properties of Real and Complex Brjuno Functions Stefano Marmi, Pierre Moussa, Jean-Christophe Yoccoz

Table of contents of volume II
You can order this book online from Springer site.

Frontiers in Number Theory, Physics and Geometry Volume 2: On Conformal Field Theory, Discrete Groups, and Renormalisation

Preface

Part I Conformal Field Theories for Strings and Branes

The Dilogarithm Function Don Zagier
Conformal Field Theory and Torsion Elements of the Bloch Group Werner Nahm
Tracks, Lie's, and Exceptional Magic Predrag Cvitanovic
Gauge Theories from D-Branes Paolo Di Vecchia, Antonella Liccardo
On Superconformal Field Theories Asso ciated to Very Attractive quartics Katrin Wendland

Part II Discrete groups and Automorphic Forms

An introduction to arithmetic groups Christophe Soulé
Automorphic forms: a physicist's survey Boris Pioline, Andrew Waldron
Strings and Arithmetic Gregory Moore
Modular curves, C*-algebras, and chaotic cosmology Matilde Marcolli
Replicable functions: an introduction John McKay, Abdellah Sebbar
Lectures on the Langlands Program and Conformal Field Theory Edward Frenkel

Part III Renormalization

A primer on Hopf algebras, Pierre Cartier
Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory Alain Connes, Matilde Marcolli
Factorization in quantum field theory: an exercise in Hopf algebras and local singularities Dirk Kreimer
Algebraic Algorithms in Perturbative Calculations Stefan Weinzierl
Multiple logarithms, algebraic cycles and trees H. Gangl, A.B. Goncharov, A. Levin

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Lectures of the Les Houches SchoolFrontiers in Number Theory, Physics and Geometry

volume I -- volume II

Lectures of the Les Houches School
Frontiers in Number Theory, Physics and Geometry