Enumerative Invariants In Algebraic Geometry And String Theory

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Enumerative Invariants in Algebraic Geometry and String Theory

Marcos Marino,Michael Thaddeus,Ravi Vakil
Enumerative Invariants in Algebraic Geometry and String Theory Book PDF

Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer
Page : 210 pages
File Size : 50,9 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540798149

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Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf

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

Marcos Marino,Michael Thaddeus,Ravi Vakil
Enumerative Invariants in Algebraic Geometry and String Theory Book PDF

Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer
Page : 210 pages
File Size : 44,9 Mb
Release : 2009-08-29
Category : Mathematics
ISBN : 3540872663

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Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf

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

Marcos Marino,Michael Thaddeus,Ravi Vakil
Enumerative Invariants in Algebraic Geometry and String Theory Book PDF

Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 49,8 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783540798132

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Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf

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

Sheldon Katz
Enumerative Geometry and String Theory Book PDF

Author : Sheldon Katz
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 54,6 Mb
Release : 2006
Category : Geometry, Enumerative
ISBN : 9780821836873

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Enumerative Geometry and String Theory by Sheldon Katz Pdf

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.

Recent Progress in Mathematics

Nam-Gyu Kang,Jaigyoung Choe,Kyeongsu Choi,Sang-hyun Kim
Recent Progress in Mathematics Book PDF

Author : Nam-Gyu Kang,Jaigyoung Choe,Kyeongsu Choi,Sang-hyun Kim
Publisher : Springer Nature
Page : 206 pages
File Size : 44,5 Mb
Release : 2022-09-30
Category : Mathematics
ISBN : 9789811937088

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Recent Progress in Mathematics by Nam-Gyu Kang,Jaigyoung Choe,Kyeongsu Choi,Sang-hyun Kim Pdf

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas. Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson–Thomas theory for Calabi–Yau 4-folds, and Vafa–Witten invariants. Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale–Kato–Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations. Simon Brendle discusses recent developments that have led to a complete classification of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension 3. Hyeonbae Kang reviews some of the developments in the Neumann–Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO. Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit “discriminant-like” affine algebraic varieties.

String-Math 2014

Vincent Bouchard:,Charles Doran,Stefan Méndez-Diez,Callum Quigley
String Math 2014 Book PDF

Author : Vincent Bouchard:,Charles Doran,Stefan Méndez-Diez,Callum Quigley
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 48,6 Mb
Release : 2016-06-10
Category : $K$-theory
ISBN : 9781470419929

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String-Math 2014 by Vincent Bouchard:,Charles Doran,Stefan Méndez-Diez,Callum Quigley Pdf

The conference String-Math 2014 was held from June 9–13, 2014, at the University of Alberta. This edition of String-Math is the first to include satellite workshops: “String-Math Summer School” (held from June 2–6, 2014, at the University of British Columbia), “Calabi-Yau Manifolds and their Moduli” (held from June 14–18, 2014, at the University of Alberta), and “Quantum Curves and Quantum Knot Invariants” (held from June 16–20, 2014, at the Banff International Research Station). This volume presents the proceedings of the conference and satellite workshops. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to modular forms and other arithmetic techniques. Articles in this book address many of these topics.

Donaldson Type Invariants for Algebraic Surfaces

Takuro Mochizuki
Donaldson Type Invariants for Algebraic Surfaces Book PDF

Author : Takuro Mochizuki
Publisher : Springer
Page : 404 pages
File Size : 42,6 Mb
Release : 2009-04-20
Category : Mathematics
ISBN : 9783540939139

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Donaldson Type Invariants for Algebraic Surfaces by Takuro Mochizuki Pdf

In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting “universal relations among invariants”, which would be a natural generalization of the “wall-crossing formula” and the “Witten conjecture” for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ̈ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.

Representation Theory, Mathematical Physics, and Integrable Systems

Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov
Representation Theory Mathematical Physics and Integrable Systems Book PDF

Author : Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov
Publisher : Springer Nature
Page : 652 pages
File Size : 48,6 Mb
Release : 2022-02-05
Category : Mathematics
ISBN : 9783030781484

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Representation Theory, Mathematical Physics, and Integrable Systems by Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov Pdf

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Radu Laza,Matthias Schütt,Noriko Yui
Calabi Yau Varieties Arithmetic Geometry and Physics Book PDF

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer
Page : 547 pages
File Size : 47,8 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9781493928309

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Calabi-Yau Varieties: Arithmetic, Geometry and Physics by Radu Laza,Matthias Schütt,Noriko Yui Pdf

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.

Orbifolds in Mathematics and Physics

Alejandro Adem,Jack Morava,Yongbin Ruan
Orbifolds in Mathematics and Physics Book PDF

Author : Alejandro Adem,Jack Morava,Yongbin Ruan
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 48,6 Mb
Release : 2002
Category : Mathematical physics
ISBN : 9780821829905

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Orbifolds in Mathematics and Physics by Alejandro Adem,Jack Morava,Yongbin Ruan Pdf

This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.

Geometry of Algebraic Curves

Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths
Geometry of Algebraic Curves Book PDF

Author : Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths
Publisher : Springer Science & Business Media
Page : 963 pages
File Size : 53,8 Mb
Release : 2011-03-10
Category : Mathematics
ISBN : 9783540693925

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Geometry of Algebraic Curves by Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths Pdf

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.

Arithmetic and Geometry Around Quantization

Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli
Arithmetic and Geometry Around Quantization Book PDF

Author : Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 52,7 Mb
Release : 2010-01-12
Category : Mathematics
ISBN : 9780817648312

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Arithmetic and Geometry Around Quantization by Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli Pdf

This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.

Algebraic Geometry

Richard Thomas
Algebraic Geometry Book PDF

Author : Richard Thomas
Publisher : American Mathematical Soc.
Page : 635 pages
File Size : 45,5 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435783

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Algebraic Geometry by Richard Thomas Pdf

This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Symplectic 4-Manifolds and Algebraic Surfaces

Fabrizio Catanese,Denis Auroux,Gang Tian,Marco Manetti,Paul Seidel,Bernd Siebert,Ivan Smith
Symplectic 4 Manifolds and Algebraic Surfaces Book PDF

Author : Fabrizio Catanese,Denis Auroux,Gang Tian,Marco Manetti,Paul Seidel,Bernd Siebert,Ivan Smith
Publisher : Springer
Page : 363 pages
File Size : 47,7 Mb
Release : 2008-04-17
Category : Mathematics
ISBN : 9783540782797

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Symplectic 4-Manifolds and Algebraic Surfaces by Fabrizio Catanese,Denis Auroux,Gang Tian,Marco Manetti,Paul Seidel,Bernd Siebert,Ivan Smith Pdf

Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.

New Techniques in Resolution of Singularities

Dan Abramovich,Anne Frühbis-Krüger,Michael Temkin,Jarosław Włodarczyk
New Techniques in Resolution of Singularities Book PDF

Author : Dan Abramovich,Anne Frühbis-Krüger,Michael Temkin,Jarosław Włodarczyk
Publisher : Springer Nature
Page : 345 pages
File Size : 55,6 Mb
Release : 2023-10-16
Category : Mathematics
ISBN : 9783031321153

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New Techniques in Resolution of Singularities by Dan Abramovich,Anne Frühbis-Krüger,Michael Temkin,Jarosław Włodarczyk Pdf

Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced. The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.