Geometry

In this book, the optimal transportation problem (OT) is described as a variational problem for absolutely continuous stochastic processes with fixed initial and terminal distributions.

The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student.

This book collects a series of important works on noncommutative harmonic analysis on homogeneous spaces and related topics.

This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and PohangThe conferences were focused on the following two related problems:*  existence of Kahler-Einstein metrics on Fano varieties*  degenerations of Fano varietieson which two famous conjectures were recently proved.

The book provides a self-contained and systematic treatment of algebraic and topological properties of convex sets in the n-dimensional Euclidean space.

This book is devoted to Hilbert's 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain.

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields.

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.

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries.

This volume honors Sir Peter Swinnerton-Dyer''s mathematical career spanning more than 60 years'' of amazing creativity in number theory and algebraic geometry.

A Fields medalist recounts his lifelong effort to uncover the geometric shape-the Calabi-Yau manifold-that may store the hidden dimensions of our universe.

This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach.

The book collects results about realization spaces of polytopes.

Spencer Bloch''s landmark lectures are finally back in print, with a new preface by the author reflecting on recent developments.

Fractalize That!

This book provides readers with an engaging explanation of the Aleksandrov problem, giving readers an overview of the process of solving Aleksandrov-Rassias problems, which are still actively studied by many mathematicians, and familiarizing readers with the details of the proof process.

The objective of this book is to provide tools for solving problems which involve cubic number fields.

This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories?

The textbook provides both beginner and experienced CAD users with the math behind the CAD.

This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians.

The Four Corners of Mathematics: A Brief History, from Pythagoras to Perelman describes the historical development of the 'big ideas' in mathematics in an accessible and intuitive manner.

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems.

This book introduces a new geometric vision of continued fractions.

This book constitutes the thoroughly refereed post-conference proceedings of the 16th Japanese Conference on Discrete and computational Geometry and Graphs, JDCDGG 2013, held in Tokyo, Japan, in September 2013.

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.

Riemannian geometry has today become a vast and important subject.

This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics.

Topology is the mathematical study of the most basic geometrical structure of a space.

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group.

The problem of "e;Shortest Connectivity"e;, which is discussed here, has a long and convoluted history.

The book explains concepts and ideas of mathematics and physics that are relevant for advanced students and researchers of condensed matter physics.

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them?

Localization of Nilpotent Groups and Spaces

He [Kronecker] was, in fact, attempting to describe and to initiate a new branch of mathematics, which would contain both number theory and alge- braic geometry as special cases.

This book consists of 16 surveys on Thurston's work and its later development.

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.