Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization

✍ Scribed by Don Zagier (auth.), Pierre Cartier, Pierre Moussa, Bernard Julia, Pierre Vanhove (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2007
• Tongue: English
• Leaves: 806
• Edition: 1
• Category: Library

✦ Synopsis

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).

✦ Table of Contents

Front Matter....Pages I-XXVIII
Front Matter....Pages I-XXVIII
The Dilogarithm Function....Pages 3-65
Conformal Field Theory and Torsion Elements of the Bloch Group....Pages 67-132
Tracks, Lie's, and Exceptional Magic....Pages 133-160
Gauge Theories from D Branes....Pages 161-222
On Superconformal Field Theories Associated to Very Attractive Quartics....Pages 223-244
Front Matter....Pages I-XXVIII
An Introduction to Arithmetic Groups....Pages 247-276
Automorphic Forms: A Physicist's Survey....Pages 277-302
Strings and Arithmetic....Pages 303-359
Modular Curves, C*-algebras, and Chaotic Cosmology....Pages 361-372
Replicable Functions: An Introduction....Pages 373-386
Lectures on the Langlands Program and Conformal Field Theory....Pages 387-533
Front Matter....Pages I-XXVIII
A Primer of Hopf Algebras....Pages 537-615
Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory....Pages 617-713
Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities....Pages 715-736
Algebraic Algorithms in Perturbative Calculations....Pages 737-757
Multiple Logarithms, Algebraic Cycles and Trees....Pages 759-774
Back Matter....Pages 775-789

✦ Subjects

Number Theory; Algebraic Geometry; Mathematical and Computational Physics