Algebraic geometry

This book is a tribute to the memory of Yuri Ivanovich Manin, who passed away on January 7, 2023.

Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view.

In this modern treatment of the topic, Rolland Trapp presents an accessible introduction to the topic of multivariable calculus, supplemented by the use of fully interactive three-dimensional graphics throughout the text.

This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory' at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions.

A NATO Advanced Study Institute entitled "e;Algebraic K-theory: Connections with Geometry and Topology"e; was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987.

This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays.

This book arose from a conference on "e;Singularities and Computer Algebra"e; which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday.

This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems.

This book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000.

The book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R.

These notes present very recent results on compact Kahler-Einstein manifolds of positive scalar curvature.

Algebraic curves and surfaces are an old topic of geometric and algebraic investigation.

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles.

The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry.

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction.

This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces.

This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces.

This book presents a unified mathematical treatment of diverse problems in thegeneral domain of robotics and associated fields using Clifford or geometric alge-bra.

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

We investigate GIT quotients of polarized curves.

In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups.

This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity.

This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68.

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Eine verständliche, konzise und immer flüssige Einführung in die Algebra, die insbesondere durch ihre sorgfältige didaktische Aufbereitung bei vielen Studenten Freunde finden wird.

This book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications.

Particles with fractional statistics interpolating betweenbosons and fermions have attracted considerable interestfrom mathematical physicists.

These notes introduce a new class of algebraic curves on Hilbert modular surfaces.

This book is about three seemingly independent areas of mathematics: combinatorial group theory, the theory of Lie algebras and affine algebraic geometry.

Etale cohomology is an important branch in arithmetic geometry.

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles.

Describes how to use coherent sheaves and cohomology to prove combinatorial and number theoretical identities over finite fields.

A collection of articles presenting the state of the art in the topic of modular forms.

This book provides an introduction to fundamental methods and techniques of algebra over ordered fields.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory.

The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups.

This monograph establishes a general context for the cohomological use of Hironaka's theorem on the resolution of singularities.

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume.

Vector Measures and Control Systems

The second edition presents schemes, simplicial sets, higher categories, model categories, derived algebraic geometry, and spectral algebraic geometry in a self-contained manner.