Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. CR geometry has become an important topic in differential geometry and the study of non-linear partial differential equations. This book discusses CR functi

Demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. This book presents an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture.

One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials, has long been known to be connected to combinatorics, representation theory and other branches of mathematics. This volume explains developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

Since the 1980s, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. A variety of different approaches to the superprocesses have emerged, yet no one approach has superseded any others. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. The emphasis is on why results are true rather than...

Arithmetic non commutative geometry uses ideas and tools from non commutative geometry to reinterpret results and constructions from number theory and arithmetic algebraic geometry. This book offers a comprehensive account of the cross fertilization betwee

This text presents a collection of small essays containing the history and the proofs of some important theorems of analysis and partial differential operators from this century. Most of the results in the book are associated with Swedish mathematicians. Also included are the Tarski-Seidenberg theorem and Wiener's classical results in harmonic analysis and an essay on the impact of distributions in analysis. All mathematical points are fully explained, but some require a certain mature understanding from the reader. This book offers full mathematical treatment, along with insight and points...

This title gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory....

Hugh Woodin is a leading figure in modern set theory, having made many contributions to the field, in particular to descriptive set theory and large cardinals. This book offers a detailed treatment of his method of the stationary tower that is generally accessible to graduate students in mathematical logic.

This book contains the latest developments in a central theme of research on analysis of one complex variable. The material is based on lectures at the University of Michigan. The exposition is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for $Hinfty$, and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem. The author clarifies how certain basic properties of the space...

This is the second volume in the new University Lecture series designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher Lectures presented by Fritz John in April 1989.