Higher Airy Structures, $mathcal {W}$ Algebras and Topological Recursion PDF Download
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Author: Gaëtan Borot
Publisher: American Mathematical Society
ISBN: 1470469065
Category : Mathematics
Languages : en
Pages : 120
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Book Description
View the abstract.
Author: Gaëtan Borot
Publisher: American Mathematical Society
ISBN: 1470469065
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
View the abstract.
Author: Gaëtan Borot
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Chiu-Chu Melissa Liu
Publisher: American Mathematical Soc.
ISBN: 1470435411
Category : Topology
Languages : en
Pages : 549
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Book Description
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.
Author: Vlatko Vedral
Publisher: Oxford University Press
ISBN: 0198815433
Category : COMPUTERS
Languages : en
Pages : 257
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Book Description
For a physicist, all the world is information. The Universe and its workings are the ebb and flow of information. We are all transient patterns of information, passing on the recipe for our basic forms to future generations using a four-letter digital code called DNA. In this engaging and mind-stretching account, Vlatko Vedral considers some of the deepest questions about the Universe and considers the implications of interpreting it in terms of information. He explains the nature of information, the idea of entropy, and the roots of this thinking in thermodynamics. He describes the bizarre effects of quantum behaviour -- effects such as 'entanglement', which Einstein called 'spooky action at a distance', and explores cutting edge work on harnessing quantum effects in hyperfast quantum computers, and how recent evidence suggests that the weirdness of the quantum world, once thought limited to the tiniest scales, may reach into the macro world. Vedral finishes by considering the answer to the ultimate question: where did all of the information in the Universe come from? The answers he considers are exhilarating, drawing upon the work of distinguished physicist John Wheeler. The ideas challenge our concept of the nature of particles, of time, of determinism, and of reality itself. This edition includes a new foreword from the author, reflecting on changes in the world of quantum information since first publication. Oxford Landmark Science books are 'must-read' classics of modern science writing which have crystallized big ideas, and shaped the way we think.
Author: Igor Rostislavovich Shafarevich
Publisher: Springer Science & Business Media
ISBN: 9783540575542
Category : Mathematics
Languages : en
Pages : 292
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Book Description
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics.
Author: Gaëtan Borot
Publisher: Springer
ISBN: 3319333798
Category : Science
Languages : en
Pages : 233
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Book Description
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.
Author: Emily Clader
Publisher: Springer
ISBN: 3319942204
Category : Mathematics
Languages : en
Pages : 625
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Book Description
This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician’s point-of-view, including such topics as polyvector fields and primitive forms, Givental’s ancestor potential, and integrable systems.
Author: Vincent Bouchard:
Publisher: American Mathematical Soc.
ISBN: 1470419920
Category : Mathematics
Languages : en
Pages : 418
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Book Description
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.
Author: Noriko Yui
Publisher: American Mathematical Soc.
ISBN: 0821844849
Category : Mathematics
Languages : en
Pages : 320
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Book Description
"This book is a testimony to the BIRS Workshop, and it covers a wide range of topics at the interface of number theory and string theory, with special emphasis on modular forms and string duality. They include the recent advances as well as introductory expositions on various aspects of modular forms, motives, differential equations, conformal field theory, topological strings and Gromov-Witten invariants, mirror symmetry, and homological mirror symmetry. The contributions are roughly divided into three categories: arithmetic and modular forms, geometric and differential equations, and physics and string theory. The book is suitable for researchers working at the interface of number theory and string theory."--BOOK JACKET.
Author: Ali Chamseddine
Publisher: Springer Nature
ISBN: 3030295974
Category : Mathematics
Languages : en
Pages : 753
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Book Description
This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.
