Enumerative Geometry and String Theory

Sheldon Katz

ISBN 10: 0821836870 / ISBN 13: 9780821836873

Editore: American Mathematical Society, US, 2006

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. Codice articolo LU-9780821836873

Riassunto:

This book is based on a series of 15 advanced undergraduate lectures given at the Park City Mathematics Institute on modern enumerative geometry. Beginning with background from classical enumerative geometry, the text's goal is to explain the rudiments of stable maps and Gromov-Witten theory and to explain connections to string theory in physics (assuming no more than a first undergraduate course in physics). Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

Product Description: Book by Sheldon Katz

Dati bibliografici

Titolo: Enumerative Geometry and String Theory
Casa editrice: American Mathematical Society, US
Data di pubblicazione: 2006
Legatura: Paperback
Condizione: New