Enumerative Invariants in Algebraic Geometry and String Theory
Title | Enumerative Invariants in Algebraic Geometry and String Theory PDF eBook |
Author | Marcos Marino |
Publisher | Springer Science & Business Media |
Pages | 219 |
Release | 2008-08-22 |
Genre | Mathematics |
ISBN | 3540798137 |
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 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 Invariants in Algebraic Geometry and String Theory
Title | Enumerative Invariants in Algebraic Geometry and String Theory PDF eBook |
Author | Marcos Marino |
Publisher | Springer |
Pages | 210 |
Release | 2009-08-29 |
Genre | Mathematics |
ISBN | 9783540872665 |
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 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.
The Moduli Space of Curves
Title | The Moduli Space of Curves PDF eBook |
Author | Robert H. Dijkgraaf |
Publisher | Springer Science & Business Media |
Pages | 570 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461242649 |
The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
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.
Calabi-Yau Varieties: Arithmetic, Geometry and Physics
Title | Calabi-Yau Varieties: Arithmetic, Geometry and Physics PDF eBook |
Author | Radu Laza |
Publisher | Springer |
Pages | 542 |
Release | 2015-08-27 |
Genre | Mathematics |
ISBN | 1493928309 |
This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.