Enumerative Geometry And String Theory
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Enumerative Geometry And String Theory
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Author : Sheldon Katz
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Enumerative Geometry And String Theory written by Sheldon Katz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Enumerative Invariants In Algebraic Geometry And String Theory
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Author : Marcos Marino
language : en
Publisher: Springer
Release Date : 2009-08-29
Enumerative Invariants In Algebraic Geometry And String Theory written by Marcos Marino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Mathematics categories.
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.
Calabi Yau Varieties Arithmetic Geometry And Physics
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Author : Radu Laza
language : en
Publisher: Springer
Release Date : 2015-08-27
Calabi Yau Varieties Arithmetic Geometry And Physics written by Radu Laza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-27 with Mathematics categories.
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.
Enumerative Invariants In Algebraic Geometry And String Theory
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Author : Marcos Marino
language : en
Publisher: Springer
Release Date : 2008-08-15
Enumerative Invariants In Algebraic Geometry And String Theory written by Marcos Marino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-15 with Mathematics categories.
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.
3264 And All That
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Author : David Eisenbud
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-14
3264 And All That written by David Eisenbud and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-14 with Mathematics categories.
3264, the mathematical solution to a question concerning geometric figures.
The Shape Of Inner Space
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Author : Shing-Tung Yau
language : en
Publisher: Hachette UK
Release Date : 2010-09-07
The Shape Of Inner Space written by Shing-Tung Yau and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-07 with Science categories.
String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where we've been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
Chern Simons Theory Matrix Models And Topological Strings
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Author : Marcos Marino
language : en
Publisher:
Release Date : 2005
Chern Simons Theory Matrix Models And Topological Strings written by Marcos Marino and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
String Math 2011
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Author : Jonathan Block
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
String Math 2011 written by Jonathan Block and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory and quantum field theory have contributed a series of profound ideas that gave rise to entirely new mathematical fields and revitalized older ones. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. A large and rapidly growing number of both mathematicians and physicists are working at the string-theoretic interface between the two academic fields. The String-Math conference series aims to bring together leading mathematicians and mathematically minded physicists working in this interface. This volume contains the proceedings of the inaugural conference in this series, String-Math 2011, which was held June 6-11, 2011, at the University of Pennsylvania.
Homological Mirror Symmetry
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Author : Anton Kapustin
language : en
Publisher: Springer Science & Business Media
Release Date : 2009
Homological Mirror Symmetry written by Anton Kapustin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
An ideal reference on the mathematical aspects of quantum field theory, this volume provides a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives.