Algebraic Geometry

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad ra...

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This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimu...

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian ...

The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible defini...

This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned ...

This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and to...

This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using gr...

The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges betwee...

The Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheave...

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common founda...

There are many interactions between noncommutative algebra and representation theory on the one hand and classical algebraic geometry on the other,...

This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular empha...

Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics...

This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain ...

This text-based on the author's popular courses at Pomona College-provides a readable, student-friendly, and somewhat sophisticated introduction to...

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. ...

This volume contains research and expository content based on a wide variety of topics within modern number theory and arithmetic geometry. Researc...

We show that the generation problem in Thompson's group F is decidable, i.e., there is an algorithm which decides if a finite set of elements of F ...

Categorifies a tensor product of two Weyl modules for quantum sl2 at a prime root of unity.

Categorifies tensor products of the fundamental representation of quantum sl2 at prime roots of unity, building upon earlier work where a tensor pr...

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in ...

Hodge theoryone of the pillars of modern algebraic geometryis a deep theory with many applications and open problems, the most enigmatic of which i...