Geometry

The characterization of combinatorial or geometric structures in terms of their groups of automorphisms has attracted considerable interest in the last decades and is now commonly viewed as a natural generalization of Felix Klein's Erlangen program(1872).

Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics.

This book provides a comprehensive introduction to the Calculus of Variations and its use in modelling mechanics and physics problems.

This book provides the foundations for geometric applications of convex cones and presents selected examples from a wide range of topics, including polytope theory, stochastic geometry, and Brunn-Minkowski theory.

This book develops a new theory in convex geometry, generalizing positive bases and related to Caratheordory's Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra)This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization.

This new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics.

This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance.

This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties.

This book discusses the changing conceptions about the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century.

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

This volume presents the beautiful memoirs of Euler, Lagrange and Lambert on geography, translated into English and put into perspective through explanatory and historical essays as well as commentaries and mathematical notes.

This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta.

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology.

The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve.

Part 1 of this popular graduate-level textbook focuses on mathematical methods involving complex analysis, determinants, and matrices, including updated and additional material covering conformal mapping.

This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra, representation theory and geometry.

This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Cordoba, Spain, on February 1-5, 2021.

This proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020.

This book gathers twenty-two papers presented at the second NLAGA-BIRS Symposium, which was held at Cap Skirring and at the Assane Seck University in Ziguinchor, Senegal, on January 25-30, 2022.

This book provides an introduction to deformation quantization and its relation to quantum field theory, with a focus on the constructions of Kontsevich and Cattaneo & Felder.

This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory.

This collection of essays aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it.

This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics.

This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field.

This volume collects papers based on talks given at the conference "e;Geometrias'19: Polyhedra and Beyond"e;, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal.

This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics.

This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point.

In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli.

The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston's heritage.

A significant number of works have set forth, over the past decades, the emphasis laid by seventeenth-century mathematicians and philosophers on motion and kinematic notions in geometry.

This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable.

This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis-Kapustin (GCK) type.

This book combines the classical and contemporary approaches to differential geometry.

This textbook introduces the special theory of relativity at a level which is accessible to undergraduate students and even high school students with a strong foundation in algebra.

This monograph explores classical electrodynamics from a geometrical perspective with a clear visual presentation throughout.

This volume features contributions from the Women in Commutative Algebra (WICA) workshop held at the Banff International Research Station (BIRS) from October 20-25, 2019, run by the Pacific Institute of Mathematical Sciences (PIMS).

This book provides an introduction to geometric invariant theory from a differential geometric viewpoint.

This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers.

This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems.

This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces.

This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud's 65th birthday.

This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics.

This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas.

The volume consists of a set of surveys on geometry in the broad sense.

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov's pivotal work in the 1980s.

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.

The ancient Greeks believed that everything in the Universe should be describable in terms of geometry.

This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets.

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry.