Frontiers in Number Theory, Physics, and Geometry II

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

Conformal Field Theories for Strings and Branes.- The Dilogarithm Function.- Conformal Field Theory and Torsion Elements of the Bloch Group.- Tracks, Lie's, and Exceptional Magic.- Gauge Theories from D Branes.- On Superconformal Field Theories Associated to Very Attractive Quartics.- Discrete Groups and Automorphic Forms.- An Introduction to Arithmetic Groups.- Automorphic Forms: A Physicist's Survey.- Strings and Arithmetic.- Modular Curves, C*-algebras, and Chaotic Cosmology.- Replicable Functions: An Introduction.- Lectures on the Langlands Program and Conformal Field Theory.- Hopf Algebras and Renormalization.- A Primer of Hopf Algebras.- Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory.- Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities.- Algebraic Algorithms in Perturbative Calculations.- Multiple Logarithms, Algebraic Cycles and Trees.