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

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Publisher : American Mathematical Soc.
ISBN 13 : 1470435411
Total Pages : 578 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topological Recursion and its Influence in Analysis, Geometry, and Topology by : Chiu-Chu Melissa Liu

Download or read book Topological Recursion and its Influence in Analysis, Geometry, and Topology written by Chiu-Chu Melissa Liu and published by American Mathematical Soc.. This book was released on 2018-11-19 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Frontiers in Geometry and Topology

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Publisher : American Mathematical Society
ISBN 13 : 147047087X
Total Pages : 320 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Frontiers in Geometry and Topology by : Paul M. N. Feehan

Download or read book Frontiers in Geometry and Topology written by Paul M. N. Feehan and published by American Mathematical Society. This book was released on 2024-07-19 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the summer school and research conference “Frontiers in Geometry and Topology”, celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1–12, 2022, at the Abdus Salam International Centre for Theoretical Physics (ICTP). The summer school featured ten lecturers and the research conference featured twenty-three speakers covering a range of topics. A common thread, reflecting Mrowka's own work, was the rich interplay among the fields of analysis, geometry, and topology. Articles in this volume cover topics including knot theory; the topology of three and four-dimensional manifolds; instanton, monopole, and Heegaard Floer homologies; Khovanov homology; and pseudoholomorphic curve theory.

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

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Publisher : American Mathematical Soc.
ISBN 13 : 1470455927
Total Pages : 480 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry by : Sergey Novikov

Download or read book Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : American Mathematical Soc.
ISBN 13 : 1470442841
Total Pages : 466 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representations of Reductive Groups by : Avraham Aizenbud

Download or read book Representations of Reductive Groups written by Avraham Aizenbud and published by American Mathematical Soc.. This book was released on 2019-02-20 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Open Problems in Algebraic Combinatorics

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Publisher : American Mathematical Society
ISBN 13 : 147047333X
Total Pages : 382 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Open Problems in Algebraic Combinatorics by : Christine Berkesch

Download or read book Open Problems in Algebraic Combinatorics written by Christine Berkesch and published by American Mathematical Society. This book was released on 2024-08-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.

Categorical, Combinatorial and Geometric Representation Theory and Related Topics

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Publisher : American Mathematical Society
ISBN 13 : 1470471175
Total Pages : 536 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Categorical, Combinatorial and Geometric Representation Theory and Related Topics by : Pramod N. Achar

Download or read book Categorical, Combinatorial and Geometric Representation Theory and Related Topics written by Pramod N. Achar and published by American Mathematical Society. This book was released on 2024-07-11 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.

Nine Mathematical Challenges: An Elucidation

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Publisher : American Mathematical Soc.
ISBN 13 : 1470454904
Total Pages : 221 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nine Mathematical Challenges: An Elucidation by : A. Kechris

Download or read book Nine Mathematical Challenges: An Elucidation written by A. Kechris and published by American Mathematical Soc.. This book was released on 2021-09-24 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : Springer Nature
ISBN 13 : 3030761908
Total Pages : 297 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Instanton Counting, Quantum Geometry and Algebra by : Taro Kimura

Download or read book Instanton Counting, Quantum Geometry and Algebra written by Taro Kimura and published by Springer Nature. This book was released on 2021-07-05 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

String-Math 2022

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Publisher : American Mathematical Society
ISBN 13 : 1470472406
Total Pages : 306 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis String-Math 2022 by : Ron Donagi

Download or read book String-Math 2022 written by Ron Donagi and published by American Mathematical Society. This book was released on 2024-04-18 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : American Mathematical Society
ISBN 13 : 1470469065
Total Pages : 120 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Higher Airy Structures, $mathcal {W}$ Algebras and Topological Recursion by : Gaëtan Borot

Download or read book Higher Airy Structures, $mathcal {W}$ Algebras and Topological Recursion written by Gaëtan Borot and published by American Mathematical Society. This book was released on 2024-05-15 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles

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Publisher : World Scientific
ISBN 13 : 9813229101
Total Pages : 412 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles by : Richard Wentworth

Download or read book The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles written by Richard Wentworth and published by World Scientific. This book was released on 2018-06-28 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.

Representation and Productive Ambiguity in Mathematics and the Sciences

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Publisher : Oxford University Press
ISBN 13 : 0199299730
Total Pages : 332 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Representation and Productive Ambiguity in Mathematics and the Sciences by : Emily R. Grosholz

Download or read book Representation and Productive Ambiguity in Mathematics and the Sciences written by Emily R. Grosholz and published by Oxford University Press. This book was released on 2007-08-30 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian 'analysis' - the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience. Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable for mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are sublty altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholtz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.

Diophantine Discoveries Fundamentals

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Publisher : N.B. Singh
ISBN 13 :
Total Pages : 63 pages
Book Rating : 4./5 ( download)

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Book Synopsis Diophantine Discoveries Fundamentals by : N.B. Singh

Download or read book Diophantine Discoveries Fundamentals written by N.B. Singh and published by N.B. Singh. This book was released on with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Diophantine Discoveries Fundamentals" is a beginner-friendly exploration of the captivating world of Diophantine equations, designed for those with no prior mathematical background. Delving into the realm of mathematical puzzles, this book offers clear and accessible explanations of Diophantine equations, starting from the basics and gradually building up the reader's understanding. Through engaging examples and straightforward language, readers are introduced to the fascinating concepts of finding whole number solutions to polynomial equations. From the historical significance of Diophantine equations to their applications in various fields such as number theory, algebra, and cryptography, this book serves as an inviting gateway for curious minds to unravel the mysteries of mathematics. Whether you're a student eager to expand your mathematical knowledge or simply someone with a passion for learning, "Diophantine Discoveries Fundamentals" provides an enjoyable and educational journey into the heart of mathematical exploration.

The Geometry of Jet Bundles

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Publisher : Cambridge University Press
ISBN 13 : 0521369487
Total Pages : 307 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis The Geometry of Jet Bundles by : D. J. Saunders

Download or read book The Geometry of Jet Bundles written by D. J. Saunders and published by Cambridge University Press. This book was released on 1989-03-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to , particularly those associated with the calculus of variations, in a modern geometric way.

Counting Surfaces

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Publisher : Springer Science & Business Media
ISBN 13 : 3764387971
Total Pages : 427 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Counting Surfaces by : Bertrand Eynard

Download or read book Counting Surfaces written by Bertrand Eynard and published by Springer Science & Business Media. This book was released on 2016-03-21 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. Mor e generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and give s the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.

Computational Homology

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Publisher : Springer Science & Business Media
ISBN 13 : 0387215972
Total Pages : 488 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Computational Homology by : Tomasz Kaczynski

Download or read book Computational Homology written by Tomasz Kaczynski and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

Guide to Programs

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Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Guide to Programs by : National Science Foundation (U.S.)

Download or read book Guide to Programs written by National Science Foundation (U.S.) and published by . This book was released on 1978 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: