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Hodge Decomposition - A Method for Solving Boundary Value Problems
Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on …
Substitution Dynamical Systems - Spectral Analysis
This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate …
Coding Theory
These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of …
Lectures on Symplectic Geometry
These notes approximately transcribe a 15-week course on symplectic geometry I taught at UC Berkeley in the Fall of 1997. The course at Berkeley was greatly inspired in content and …
Diophantine Approximation and Transcendence Theory
The Atiyah-Singer Index Theorem
Noncommutative Stationary Processes
Quantum probability and the theory of operator algebras are both concerned with the study of noncommutative dynamics. Focusing on stationary processes with discrete-time parameter, …
Hodge Cycles, Motives, and Shimura Varieties
This volume collects six related articles. The first is the notes (written by J.S. Milne) of a major part of the seminar "Periodes des Int~grales Abeliennes" given by P. Deligne at …
Entropy Methods for the Boltzmann Equation
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction …
Kinetic Theories and the Boltzmann Equation
Regularity Estimates for Nonlinear Elliptic and Parabolic Problems
The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still …