Topological Recursion And Its Influence In Analysis Geometry And Topology

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Topological Recursion and its Influence in Analysis, Geometry, and Topology

Chiu-Chu Melissa Liu,Motohico Mulase
Topological Recursion and its Influence in Analysis Geometry and Topology Book PDF

Author : Chiu-Chu Melissa Liu,Motohico Mulase
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 50,6 Mb
Release : 2018-11-19
Category : Topology
ISBN : 9781470435417

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Topological Recursion and its Influence in Analysis, Geometry, and Topology by Chiu-Chu Melissa Liu,Motohico Mulase Pdf

This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina. The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces. Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwitz numbers and Grothendieck's dessins d'enfants, Gromov-Witten invariants, the A-polynomials and colored polynomial invariants of knots, WKB analysis, and quantization of Hitchin moduli spaces. In addition to establishing these topics, the volume includes survey papers on the most recent key accomplishments: discovery of the unexpected relation to semi-simple cohomological field theories and a solution to the remodeling conjecture. It also provides a glimpse into the future research direction; for example, connections with the Airy structures, modular functors, Hurwitz-Frobenius manifolds, and ELSV-type formulas.

Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry

Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Integrability Quantization and Geometry II Quantum Theories and Algebraic Geometry Book PDF

Author : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 45,6 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455927

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Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Representations of Reductive Groups

Avraham Aizenbud,Dmitry Gourevitch,David Kazhdan,Erez M. Lapid
Representations of Reductive Groups Book PDF

Author : Avraham Aizenbud,Dmitry Gourevitch,David Kazhdan,Erez M. Lapid
Publisher : American Mathematical Soc.
Page : 450 pages
File Size : 46,5 Mb
Release : 2019-02-20
Category : Representations of algebras
ISBN : 9781470442842

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Representations of Reductive Groups by Avraham Aizenbud,Dmitry Gourevitch,David Kazhdan,Erez M. Lapid Pdf

This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11–16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem. The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope. The themes include representations of p -adic groups and Hecke algebras in all characteristics, representations of real groups and supergroups, theta correspondence, and automorphic forms.

Nine Mathematical Challenges: An Elucidation

A. Kechris,N. Makarov,D. Ramakrishnan,X. Zhu
Nine Mathematical Challenges An Elucidation Book PDF

Author : A. Kechris,N. Makarov,D. Ramakrishnan,X. Zhu
Publisher : American Mathematical Soc.
Page : 221 pages
File Size : 41,8 Mb
Release : 2021-09-24
Category : Education
ISBN : 9781470454906

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Nine Mathematical Challenges: An Elucidation by A. Kechris,N. Makarov,D. Ramakrishnan,X. Zhu Pdf

This volume stems from the Linde Hall Inaugural Math Symposium, held from February 22–24, 2019, at California Institute of Technology, Pasadena, California. The content isolates and discusses nine mathematical problems, or sets of problems, in a deep way, but starting from scratch. Included among them are the well-known problems of the classification of finite groups, the Navier-Stokes equations, the Birch and Swinnerton-Dyer conjecture, and the continuum hypothesis. The other five problems, also of substantial importance, concern the Lieb–Thirring inequalities, the equidistribution problems in number theory, surface bundles, ramification in covers and curves, and the gap and type problems in Fourier analysis. The problems are explained succinctly, with a discussion of what is known and an elucidation of the outstanding issues. An attempt is made to appeal to a wide audience, both in terms of the field of expertise and the level of the reader.

Instanton Counting, Quantum Geometry and Algebra

Taro Kimura
Instanton Counting Quantum Geometry and Algebra Book PDF

Author : Taro Kimura
Publisher : Springer Nature
Page : 297 pages
File Size : 40,7 Mb
Release : 2021-07-05
Category : Science
ISBN : 9783030761905

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Instanton Counting, Quantum Geometry and Algebra by Taro Kimura Pdf

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

Topological Persistence in Geometry and Analysis

Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang
Topological Persistence in Geometry and Analysis Book PDF

Author : Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 51,6 Mb
Release : 2020-05-11
Category : Education
ISBN : 9781470454951

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Topological Persistence in Geometry and Analysis by Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang Pdf

The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.

String-Math 2022

Ron Donagi,Adrian Langer,Piotr Sułkowski,Katrin Wendland
String Math 2022 Book PDF

Author : Ron Donagi,Adrian Langer,Piotr Sułkowski,Katrin Wendland
Publisher : American Mathematical Society
Page : 306 pages
File Size : 44,9 Mb
Release : 2024-04-18
Category : Mathematics
ISBN : 9781470472405

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String-Math 2022 by Ron Donagi,Adrian Langer,Piotr Sułkowski,Katrin Wendland Pdf

This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.

Higher Airy Structures, $mathcal {W}$ Algebras and Topological Recursion

Gaëtan Borot,Vincent Bouchard,Nitin K. Chidambaram,Thomas Creutzig,Dmitry Noshchenko
Higher Airy Structures mathcal W Algebras and Topological Recursion Book PDF

Author : Gaëtan Borot,Vincent Bouchard,Nitin K. Chidambaram,Thomas Creutzig,Dmitry Noshchenko
Publisher : American Mathematical Society
Page : 120 pages
File Size : 48,9 Mb
Release : 2024-05-15
Category : Mathematics
ISBN : 9781470469061

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Higher Airy Structures, $mathcal {W}$ Algebras and Topological Recursion by Gaëtan Borot,Vincent Bouchard,Nitin K. Chidambaram,Thomas Creutzig,Dmitry Noshchenko Pdf

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New Scientific Applications of Geometry and Topology

De Witt L. Sumners,Nicholas R. Cozzarelli
New Scientific Applications of Geometry and Topology Book PDF

Author : De Witt L. Sumners,Nicholas R. Cozzarelli
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 50,5 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855026

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New Scientific Applications of Geometry and Topology by De Witt L. Sumners,Nicholas R. Cozzarelli Pdf

Geometry and topology are subjects generally considered to be "pure" mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.

Topology

Solomon Lefschetz
Topology Book PDF

Author : Solomon Lefschetz
Publisher : American Mathematical Soc.
Page : 428 pages
File Size : 54,6 Mb
Release : 1930-12-31
Category : Mathematics
ISBN : 9780821846032

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Topology by Solomon Lefschetz Pdf

Lefschetz's Topology was written in the period in between the beginning of topology, by Poincare, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of algebraic varieties. He also gives applications to vector distributions, complex spaces, and Kronecker's characteristic theory.

Topology and Geometry - Rohlin Seminar

Oleg Y. Viro
Topology and Geometry Rohlin Seminar Book PDF

Author : Oleg Y. Viro
Publisher : Springer
Page : 582 pages
File Size : 40,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540459583

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Topology and Geometry - Rohlin Seminar by Oleg Y. Viro Pdf

This volume is a collection of papers dedicated to the memory of V. A. Rohlin (1919-1984) - an outstanding mathematician and the founder of the Leningrad topological school. It includes survey and research papers on topology of manifolds, topological aspects of the theory of complex and real algebraic varieties, topology of projective configuration spaces and spaces of convex polytopes.

Topological Analysis

Gordon Thomas Whyburn
Topological Analysis Book PDF

Author : Gordon Thomas Whyburn
Publisher : Princeton University Press
Page : 138 pages
File Size : 40,7 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400879335

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Topological Analysis by Gordon Thomas Whyburn Pdf

Topological analysis consists of those basic theorems of analysis which are essentially topological in character, developed and proved entirely by topological and pseudotopological methods. The objective of this volume is the promotion, encouragement, and stimulation of the interaction between topology and analysis-to the benefit of both. Originally published in 1964. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Basic Topology 2

Avishek Adhikari,Mahima Ranjan Adhikari
Basic Topology 2 Book PDF

Author : Avishek Adhikari,Mahima Ranjan Adhikari
Publisher : Springer
Page : 366 pages
File Size : 51,9 Mb
Release : 2022-03-02
Category : Mathematics
ISBN : 9811665761

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Basic Topology 2 by Avishek Adhikari,Mahima Ranjan Adhikari Pdf

This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.

Recent Progress in General Topology III

K.P. Hart,J. van Mill,P. Simon
Recent Progress in General Topology III Book PDF

Author : K.P. Hart,J. van Mill,P. Simon
Publisher : Springer Science & Business Media
Page : 903 pages
File Size : 43,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9789462390249

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Recent Progress in General Topology III by K.P. Hart,J. van Mill,P. Simon Pdf

The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

Classical Topology and Combinatorial Group Theory

John Stillwell
Classical Topology and Combinatorial Group Theory Book PDF

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461243724

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Classical Topology and Combinatorial Group Theory by John Stillwell Pdf

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.