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Enumerative Geometry and String Theory
 
Sheldon Katz University of Illinois at Urbana-Champaign, Urbana, IL
Front Cover for Enumerative Geometry and String Theory
Available Formats:
Softcover ISBN: 978-0-8218-3687-3
Product Code: STML/32
206 pp 
List Price: $41.00
Individual Price: $32.80
Electronic ISBN: 978-1-4704-2143-4
Product Code: STML/32.E
206 pp 
List Price: $38.00
Individual Price: $30.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $61.50
Front Cover for Enumerative Geometry and String Theory
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  • Front Cover for Enumerative Geometry and String Theory
  • Back Cover for Enumerative Geometry and String Theory
Enumerative Geometry and String Theory
Sheldon Katz University of Illinois at Urbana-Champaign, Urbana, IL
Available Formats:
Softcover ISBN:  978-0-8218-3687-3
Product Code:  STML/32
206 pp 
List Price: $41.00
Individual Price: $32.80
Electronic ISBN:  978-1-4704-2143-4
Product Code:  STML/32.E
206 pp 
List Price: $38.00
Individual Price: $30.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $61.50
  • Book Details
     
     
    Student Mathematical Library
    IAS/Park City Mathematics Subseries
    Volume: 322006
    MSC: 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. 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.
    Readership

    Undergraduate 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
  • 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
  • Request Review Copy
  • Get Permissions
IAS/Park City Mathematics Subseries
Volume: 322006
MSC: 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. 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.
Readership

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 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
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