FRONTIERS IN NUMBER THEORY, PHYSICS, AND GEOMETRY II

By T. FILAM

CONTENTS PART I 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 PART II 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 PART III 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