**Student Mathematical Library**

Volume: 32;
2006;
206 pp;
Softcover

MSC: Primary 14;

Print ISBN: 978-0-8218-3687-3

Product Code: STML/32

List Price: $38.00

Individual Price: $30.40

**Electronic ISBN: 978-1-4704-2143-4
Product Code: STML/32.E**

List Price: $38.00

Individual Price: $30.40

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#### Supplemental Materials

# Enumerative Geometry and String Theory

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*Sheldon Katz*

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.

This book is published in cooperation with IAS/Park City Mathematics Institute

#### Table of Contents

# Table of Contents

## Enumerative Geometry and String Theory

- Cover Cover11 free
- Chapter 1. Warming up to enumerative geometry 12 free
- Chapter 2. Enumerative geometry in the projective plane 1314
- Chapter 3. Stable maps and enumerative geometry 2728
- Chapter 4. Crash course in topology and manifolds 4344
- Chapter 5. Crash course in 𝐶^{∞} manifolds and cohomology 5758
- Chapter 6. Cellular decompositions and line bundles 7778
- Chapter 7. Enumerative geometry of lines 9596
- Chapter 8. Excess intersection 111112
- Chapter 9. Rational curves on the quintic threefold 125126
- Chapter 10. Mechanics 135136
- Chapter 11. Introduction to supersymmetry 145146
- Chapter 12. Introduction to string theory 157158
- Chapter 13. Topological quantum field theory 173174
- Chapter 14. Quantum cohomology and enumerative geometry 185186
- Back Cover Back Cover1226

#### Readership

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

#### 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 self-study 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