Enumerative Geometry and String Theory
Title | Enumerative Geometry and String Theory PDF eBook |
Author | Sheldon Katz |
Publisher | American Mathematical Soc. |
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.
3264 and All That
Title | 3264 and All That PDF eBook |
Author | David Eisenbud |
Publisher | Cambridge University Press |
Pages | 633 |
Release | 2016-04-14 |
Genre | Mathematics |
ISBN | 1107017084 |
3264, the mathematical solution to a question concerning geometric figures.
Enumerative Invariants in Algebraic Geometry and String Theory
Title | Enumerative Invariants in Algebraic Geometry and String Theory PDF eBook |
Author | Marcos Marino |
Publisher | Springer |
Pages | 219 |
Release | 2008-08-15 |
Genre | Mathematics |
ISBN | 3540798145 |
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Enumerative Algebraic Geometry
Title | Enumerative Algebraic Geometry PDF eBook |
Author | Steven L. Kleiman |
Publisher | American Mathematical Soc. |
Pages | 292 |
Release | 1991 |
Genre | Mathematics |
ISBN | 0821851314 |
1989 marked the 150th anniversary of the birth of the great Danish mathematician Hieronymus George Zeuthen. Zeuthen's name is known to every algebraic geometer because of his discovery of a basic invariant of surfaces. However, he also did fundamental research in intersection theory, enumerative geometry, and the projective geometry of curves and surfaces. Zeuthen's extraordinary devotion to his subject, his characteristic depth, thoroughness, and clarity of thought, and his precise and succinct writing style are truly inspiring. During the past ten years or so, algebraic geometers have reexamined Zeuthen's work, drawing from it inspiration and new directions for development in the field. The 1989 Zeuthen Symposium, held in the summer of 1989 at the Mathematical Institute of the University of Copenhagen, provided a historic opportunity for mathematicians to gather and examine those areas in contemporary mathematical research which have evolved from Zeuthen's fruitful ideas. This volume, containing papers presented during the symposium, as well as others inspired by it, illuminates some currently active areas of research in enumerative algebraic geometry.
Quantum Field Theory, Supersymmetry, and Enumerative Geometry
Title | Quantum Field Theory, Supersymmetry, and Enumerative Geometry PDF eBook |
Author | Daniel S. Freed |
Publisher | American Mathematical Soc. |
Pages | 297 |
Release | 2006 |
Genre | Mathematics |
ISBN | 0821834312 |
This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, and Enumerative Geometry. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics.
Handbook of Enumerative Combinatorics
Title | Handbook of Enumerative Combinatorics PDF eBook |
Author | Miklos Bona |
Publisher | CRC Press |
Pages | 1073 |
Release | 2015-03-24 |
Genre | Mathematics |
ISBN | 1482220865 |
Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he
Tropical Algebraic Geometry
Title | Tropical Algebraic Geometry PDF eBook |
Author | Ilia Itenberg |
Publisher | Springer Science & Business Media |
Pages | 113 |
Release | 2009-05-30 |
Genre | Mathematics |
ISBN | 3034600488 |
These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.