Geometry

Conformal groups play a key role in geometry and spin structures.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

The main goal of the book is to present a proof of the following.

This book introduces geometric spectral theory in the context of Riemann surfaces.

Classical mechanics is a chief example of the scientific method organizing a "e;complex"e;collection of information into theoretically rigorous, unifying principles; in this sense, mechanics represents one of the highest forms of mathematical modeling.

This volume uses a unified approach to representation theory and automorphic forms.

This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established.

The term convexity used to describe these lectures given at the Univer- sity of Lund in 1991-92 should be understood in a wide sense.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory.

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

This volume contains the first two out of four chapters which are intended to survey a large part of the theory of theta functions.

Alexander Grothendieck's sixtieth birthday and originally published in 1990.

Alexander Grothendieck's sixtieth birthday and originally published in 1990.

Alexander Grothendieck's sixtieth birthday and originally published in 1990.

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics.

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics- and in theoretical physics such as quantum field theory and string theory.

Algebraic K-Theory has become an increasingly active area of research.

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.

Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque.

Algebra, Arithmetic, and Geometry: In Honor of Yu.

Algebra, Arithmetic, and Geometry: In Honor of Yu.

This volume offers a collection of non-trivial, unconventional problems that require deep insight and imagination to solve.

One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.

Hideki Omori is widely recognized as one of the world's most creative and original mathematicians.

D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory.

This text presents differential forms from a geometric perspective accessible at the undergraduate level.

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory.

Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector.

This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology.

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology.

The study of CR manifolds lies at the intersection of three main mathematical disciplines, partial differential equations: complex analysis in several complex variables, and differential geometry.

This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?

Dedicated to Anthony Joseph, this volume contains surveys and invited articles by leading specialists in representation theory.

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds.

Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization.

A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory.

Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups).

The field of convex geometry has become a fertile subject of mathematical activity in the past few decades.

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject.

This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the reader only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed.

Complex variables is a precise, elegant, and captivating subject.

103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team.

Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A.

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.

This volume contains research and survey articles by well known and respected mathematicians describing recent developments and research trends in differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields.

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics.

One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields.