Algebra, Geometry, and Physics in the 21st Century

by Denis Auroux
Algebra, Geometry, and Physics in the 21st Century
Author: Denis Auroux
Publisher: Birkhäuser
Total Pages: 368
Release: 2017-07-27
Genre: Mathematics
ISBN: 3319599399
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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

Mathematics Into the Twenty-first Century

by American Mathematical Society
Mathematics Into the Twenty-first Century
Author: American Mathematical Society
Publisher: American Mathematical Soc.
Total Pages: 514
Release: 1992
Genre: Mathematics
ISBN: 9780821801673
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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.

Sheaves on Manifolds

by Masaki Kashiwara
Sheaves on Manifolds
Author: Masaki Kashiwara
Publisher: Springer Science & Business Media
Total Pages: 522
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662026619
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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.

Curvature in Mathematics and Physics

by Shlomo Sternberg
Curvature in Mathematics and Physics
Author: Shlomo Sternberg
Publisher: Courier Corporation
Total Pages: 418
Release: 2013-04-17
Genre: Mathematics
ISBN: 0486292711
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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.

Fifty Years of Mathematical Physics

by Molin Ge
Fifty Years of Mathematical Physics
Author: Molin Ge
Publisher: World Scientific Publishing Company
Total Pages: 596
Release: 2016-02-16
Genre: Science
ISBN: 9814340960
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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.

New Foundations in Mathematics

by Garret Sobczyk
New Foundations in Mathematics
Author: Garret Sobczyk
Publisher: Springer Science & Business Media
Total Pages: 373
Release: 2012-10-26
Genre: Mathematics
ISBN: 0817683852
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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.

The Shape of Inner Space

by Shing-Tung Yau
The Shape of Inner Space
Author: Shing-Tung Yau
Publisher: Il Saggiatore
Total Pages: 398
Release: 2010-09-07
Genre: Mathematics
ISBN: 0465020232
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The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

Homotopical Algebraic Geometry II: Geometric Stacks and Applications

by Bertrand Toën
Homotopical Algebraic Geometry II: Geometric Stacks and Applications
Author: Bertrand Toën
Publisher: American Mathematical Soc.
Total Pages: 242
Release: 2008
Genre: Mathematics
ISBN: 0821840991
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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.

A History of Algebraic and Differential Topology, 1900 - 1960

by Jean Dieudonné
A History of Algebraic and Differential Topology, 1900 - 1960
Author: Jean Dieudonné
Publisher: Springer Science & Business Media
Total Pages: 666
Release: 2009-09-01
Genre: Mathematics
ISBN: 0817649077
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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