Softcover ISBN:  9780821836873 
Product Code:  STML/32 
206 pp 
List Price:  $41.00 
Individual Price:  $32.80 
Electronic ISBN:  9781470421434 
Product Code:  STML/32.E 
206 pp 
List Price:  $38.00 
Individual Price:  $30.40 

Book DetailsStudent Mathematical LibraryIAS/Park City Mathematics SubseriesVolume: 32; 2006MSC: Primary 14;
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. Centuryold 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.This book is published in cooperation with IAS/Park City Mathematics Institute.ReadershipUndergraduate and graduate students interested in algebraic geometry or in mathematical physics.

Table of Contents

Chapters

Chapter 1. Warming up to enumerative geometry

Chapter 2. Enumerative geometry in the projective plane

Chapter 3. Stable maps and enumerative geometry

Chapter 4. Crash course in topology and manifolds

Chapter 5. Crash course in $C^\infty $ manifolds and cohomology

Chapter 6. Cellular decompositions and line bundles

Chapter 7. Enumerative geometry of lines

Chapter 8. Excess intersection

Chapter 9. Rational curves on the quintic threefold

Chapter 10. Mechanics

Chapter 11. Introduction to supersymmetry

Chapter 12. Introduction to string theory

Chapter 13. Topological quantum field theory

Chapter 14. Quantum cohomology and enumerative geometry


Additional Material

Reviews

The most accessible portal into very exciting recent material.
CHOICE Magazine 
The book contains a lot of extra material that was not included in the original fifteen lectures. It is a nicely and intuitively written remarkable little booklet covering a huge amount of interesting material describing a beautiful area, where modern mathematics and theoretical physics meet. It can give inspiration to teachers for a lecture series on the topic as well as a chance for selfstudy by students.
EMS Newsletter 
It is a welcome addition to the spectrum of available references on the topic and ideal for someone between undergraduate and beginning graduate education who wants to know more about this exciting field or for more advanced students who would like to see how the pieces of the puzzle fit together.
Mathematical Reviews


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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. Centuryold 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.
Undergraduate and graduate students interested in algebraic geometry or in mathematical physics.

Chapters

Chapter 1. Warming up to enumerative geometry

Chapter 2. Enumerative geometry in the projective plane

Chapter 3. Stable maps and enumerative geometry

Chapter 4. Crash course in topology and manifolds

Chapter 5. Crash course in $C^\infty $ manifolds and cohomology

Chapter 6. Cellular decompositions and line bundles

Chapter 7. Enumerative geometry of lines

Chapter 8. Excess intersection

Chapter 9. Rational curves on the quintic threefold

Chapter 10. Mechanics

Chapter 11. Introduction to supersymmetry

Chapter 12. Introduction to string theory

Chapter 13. Topological quantum field theory

Chapter 14. Quantum cohomology and enumerative geometry

The most accessible portal into very exciting recent material.
CHOICE Magazine 
The book contains a lot of extra material that was not included in the original fifteen lectures. It is a nicely and intuitively written remarkable little booklet covering a huge amount of interesting material describing a beautiful area, where modern mathematics and theoretical physics meet. It can give inspiration to teachers for a lecture series on the topic as well as a chance for selfstudy by students.
EMS Newsletter 
It is a welcome addition to the spectrum of available references on the topic and ideal for someone between undergraduate and beginning graduate education who wants to know more about this exciting field or for more advanced students who would like to see how the pieces of the puzzle fit together.
Mathematical Reviews