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Algebra, Geometry, and Physics in the 21st Century

Author : Denis Auroux

Publisher : Birkhäuser

Page : 368 pages

File Size : 41,27 MB

Release : 2017-07-27

Category : Mathematics

ISBN : 3319599399

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Book Description

This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren



Sheaves on Manifolds

Author : Masaki Kashiwara

Publisher : Springer Science & Business Media

Page : 522 pages

File Size : 12,60 MB

Release : 2013-03-14

Category : Mathematics

ISBN : 3662026619

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Book Description

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.



Mathematics Into the Twenty-first Century

Author : American Mathematical Society

Publisher : American Mathematical Soc.

Page : 514 pages

File Size : 36,7 MB

Release : 1992

Category : Mathematics

ISBN : 9780821801673

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Book Description

In the summer of 1988 in Providence, the AMS celebrated its centennial with a wide range of mathematical activities. Among those was a symposium, Mathematics into the Twenty-first Century, which brought together a number of the top research mathematicians who will likely have a significant impact on the mathematics of this century. This book contains the lectures presented by 16 of the 18 individuals who spoke during the symposium. Written by some of the major international figures in mathematical research, this group of articles covers a panorama of the vital areas of mathematics at the turn of the 21st century and gives the general mathematical reader a broad perspective on some of the major trends in research.



New Foundations in Mathematics

Author : Garret Sobczyk

Publisher : Springer Science & Business Media

Page : 373 pages

File Size : 24,63 MB

Release : 2012-10-26

Category : Mathematics

ISBN : 0817683852

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Book Description

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.



A History of Algebraic and Differential Topology, 1900 - 1960

Author : Jean Dieudonné

Publisher : Springer Science & Business Media

Page : 666 pages

File Size : 29,56 MB

Release : 2009-09-01

Category : Mathematics

ISBN : 0817649077

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Book Description

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet



Fifty Years of Mathematical Physics

Author : Molin Ge

Publisher : World Scientific Publishing Company

Page : 596 pages

File Size : 18,32 MB

Release : 2016-02-16

Category : Science

ISBN : 9814340960

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Book Description

This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.



Homotopical Algebraic Geometry II: Geometric Stacks and Applications

Author : Bertrand Toën

Publisher : American Mathematical Soc.

Page : 242 pages

File Size : 43,77 MB

Release : 2008

Category : Mathematics

ISBN : 0821840991

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Book Description

This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.



Methods of Homological Algebra

Author : Sergei I. Gelfand

Publisher : Springer Science & Business Media

Page : 388 pages

File Size : 30,45 MB

Release : 2013-04-17

Category : Mathematics

ISBN : 3662032201

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Book Description

Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.



Curvature in Mathematics and Physics

Author : Shlomo Sternberg

Publisher : Courier Corporation

Page : 418 pages

File Size : 36,77 MB

Release : 2013-04-17

Category : Mathematics

ISBN : 0486292711

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Book Description

Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.



Real Algebraic Geometry

Author : Vladimir I. Arnold

Publisher : Springer Science & Business Media

Page : 113 pages

File Size : 49,21 MB

Release : 2013-04-15

Category : Mathematics

ISBN : 3642362435

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Book Description

This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).