In this comprehensive volume, the authors introduce important developments at the intersection of probability theory and mathematical physics: the Gaussian free field, Gaussian multiplicative chaos and Liouville quantum gravity.  Meer

The field of random walks on groups is re-emerging with many new ideas and exciting research. This book contains a comprehensive introduction for researchers new to the field.  Meer

Long anticipated, this work focuses on sieve methods and their applications to areas such as the gaps between prime numbers, large values of Dirichlet polynomials, and zero density estimates.  Meer

This comprehensive introduction to number theory will reward students and researchers with its insight and thoroughness. Suitable for course use and self-study, it avoids unnecessary abstraction and provides a wealth of thought-provoking examples and problems.  Meer

This book introduces convex polytopes and their graphs, alongside the results and methodology required to study them. Including background material, open problems, and cutting-edge research, this is the ideal book for readers new to the area.  Meer

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike.  Meer

This detailed introduction to cubic hypersurfaces and all the techniques needed to study them leads the reader from classical topics to recent developments studying four-dimensional cubic hypersurfaces.  Meer

Abelian model categories are receiving more attention in contemporary research. Including clear diagrammatic proofs, the book provides an elementary treatment of the foundations of abelian and exact model categories.  Meer

Oriented matroids appear throughout discrete geometry and have applications in algebra, topology, physics, and data analysis. This introductory text is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics.  Meer

This comprehensive introduction to functional analysis covers both the abstract theory and applications. With carefully written out proofs, more than 300 problems, and appendices covering prerequisites, this self-contained volume can be used as a text for a graduate-level course and as a reference text for researchers in the field.  Meer

The first graduate-level introduction to the finite generation theorem of the canonical ring, a major achievement of modern algebraic geometry. Largely self-contained, this text explains the basics of minimal model theory, covering all the progress of the last three decades and assuming only the basics in algebraic geometry.  Meer

Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics.  Meer

Discrete structures, like DNA sequences and the internet, are complex objects created from indivisible parts. Now more accessible to graduate students, this book introduces multivariate generating functions, which are used to create computational tools to detect and understand patterns in such structures.  Meer

An introduction to type theory and the univalence axiom, aimed at advanced undergraduate and graduate students of mathematics and computer science with an interest in the foundations and formalization of mathematics.  Meer