Porter Lectures

Shafarevich Maps and Automorphic Forms János Kollár

The aim of this book is to study various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups. This approach allows for much interplay between methods of algebraic geometry...

The Geometry and Dynamics of Magnetic Monopoles Michael Francis Atiyah and Nigel Hitchin

Systems governed by non-linear differential equations are of fundamental importance in all branches of science, but our understanding of them is still extremely limited. In this book a particular system, describing the interaction of...

Recurrence in Ergodic Theory and Combinatorial Number Theory Harry Furstenberg

Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number...

Topics in Non-Commutative Geometry Yuri I. Manin

There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off...

Szegő's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials Barry Simon

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and...

Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space Shmuel Weinberger

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex...