Progress in Mathematics

This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory …

In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann …

This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area.
Written in a clear and appealing style …

The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more …

This monograph presents an approachable proof of Mirzakhani’s curve counting theorem, both for simple and non-simple curves. Designed to welcome readers to the area, the presentation builds intuition with elementary examples before progressing to …

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many …

This book is an outgrowth of the conference “Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods” that was held in Paris in May 2016. Gathering contributions by leading experts in the field …

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem …

This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics. Synthesizing research from the last forty years, the author aims for accessibility by …

This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and …

The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is …

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the …

This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of …

This is the revised second edition of the well-received book by the first two authors. It offers a systematic treatment of the theory of vector bundles with integrable connection on smooth algebraic varieties over a field of characteristic 0.

This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over …

This book focuses on a selection of special topics, with emphasis on past and present research of the authors on “canonical” Riemannian metrics on smooth manifolds.

On the backdrop of the fundamental contributions given by many experts in the …

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a …

This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The …

This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the …

The present monograph develops a unified theory of Steinberg groups, independent of matrix representations, based on the theory of Jordan pairs and the theory of 3-graded locally finite root systems.
The development of this approach occurs over six …