Schubert Calculus: an Algebraic Introduction
Author | : Letterio Gatto |
Publisher | : |
Total Pages | : 121 |
Release | : 2005 |
Genre | : |
ISBN | : 9788524402272 |
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Author | : Letterio Gatto |
Publisher | : |
Total Pages | : 121 |
Release | : 2005 |
Genre | : |
ISBN | : 9788524402272 |
Author | : Jianxun Hu |
Publisher | : Springer Nature |
Total Pages | : 367 |
Release | : 2020-10-24 |
Genre | : Mathematics |
ISBN | : 9811574510 |
This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6–10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.
Author | : Thomas Lam |
Publisher | : Springer |
Total Pages | : 226 |
Release | : 2014-06-05 |
Genre | : Mathematics |
ISBN | : 1493906828 |
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.
Author | : Ezra Miller |
Publisher | : Springer Science & Business Media |
Total Pages | : 442 |
Release | : 2005-06-21 |
Genre | : Mathematics |
ISBN | : 9780387237077 |
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Author | : John Gilbert Hocking |
Publisher | : |
Total Pages | : 904 |
Release | : 1970 |
Genre | : Mathematics |
ISBN | : |
Author | : Sheldon Katz |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821836870 |
Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. Century-old problems of enumerating geometric configurations have now been solved using new and deep mathematical techniques inspired by physics! The book begins with an insightful introduction to enumerative geometry. From there, the goal becomes explaining the more advanced elements of enumerative algebraic geometry. Along the way, there are some crash courses on intermediate topics which are essential tools for the student of modern mathematics, such as cohomology and other topics in geometry. The physics content assumes nothing beyond a first undergraduate course. The focus is on explaining the action principle in physics, the idea of string theory, and how these directly lead to questions in geometry. Once these topics are in place, the connection between physics and enumerative geometry is made with the introduction of topological quantum field theory and quantum cohomology.
Author | : David Eisenbud |
Publisher | : Cambridge University Press |
Total Pages | : 633 |
Release | : 2016-04-14 |
Genre | : Mathematics |
ISBN | : 1107017084 |
3264, the mathematical solution to a question concerning geometric figures.
Author | : David A. Cox |
Publisher | : Springer Science & Business Media |
Total Pages | : 513 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475769113 |
An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Author | : W. Fulton |
Publisher | : Springer Science & Business Media |
Total Pages | : 483 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662024217 |
From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.