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Author : Jonny Evans
Publisher : Cambridge University Press
Page : 241 pages
File Size : 40,7 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781009372626
Comprehensive and visual introduction to the geometry of 4-dimensional symplectic manifolds via 2-dimensional almost-toric diagrams.
Author : Ron Donagi,Tony Pantev
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 53,5 Mb
Release : 2008
Category : Calabi-Yau manifolds
ISBN : 9780821840924
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O} DEGREES{\times}$ gerbe over a genus one fibration which is a twisted form
Author : M. J. D. Hamilton,D. Kotschick
Publisher : Cambridge University Press
Page : 200 pages
File Size : 46,9 Mb
Release : 2023-12-21
Category : Mathematics
ISBN : 9781108905619
This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.
Author : Amaury Freslon
Publisher : Cambridge University Press
Page : 302 pages
File Size : 45,7 Mb
Release : 2023-07-27
Category : Mathematics
ISBN : 9781009345682
Author : Daniel Sanz-Alonso,Andrew Stuart,Armeen Taeb
Publisher : Cambridge University Press
Page : 227 pages
File Size : 42,6 Mb
Release : 2023-08-10
Category : Computers
ISBN : 9781009414326
A clear and concise mathematical introduction to the subjects of inverse problems and data assimilation, and their inter-relations.
Author : Spiro Karigiannis,Naichung Conan Leung,Jason D. Lotay
Publisher : Springer Nature
Page : 392 pages
File Size : 42,6 Mb
Release : 2020-05-26
Category : Mathematics
ISBN : 9781071605776
This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.
Author : Cumrun Vafa,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 392 pages
File Size : 45,8 Mb
Release : 2001
Category : Mathematics
ISBN : 0821821598
The 16 articles presented here are based on lectures given at the Winter School on Mirror Symmetry held at Harvard University in January 1999. They represent recent progress and new directions in the field. Specific topics include Floer homology and mirror symmetry, special Lagrange fibrations, special Lagrangian submanifolds, and local mirror symmetry at higher genus. Other topics include homological mirror symmetry with higher products, categorical mirror symmetry in the elliptic curve, Lagrangian torus fibration of quintic hypersurfaces, mirror symmetry and T-duality, and mirror symmetry and actions of Braid groups on derived categories. This work lacks a subject index. c. Book News Inc.
Author : Lotte Hollands
Publisher : Amsterdam University Press
Page : 310 pages
File Size : 49,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9789085550204
This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded in string theory. Secondly, this model is generalized to a web of dualities connecting topological string theory and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann surface. This description yields a new perspective on topological string theory in terms of a KP integrable system based on a quantum curve. Thirdly, this thesis describes a geometric analysis of wall-crossing in N=4 string theory. And lastly, it offers a novel approach to constuct metastable vacua in type IIB string theory.
Author : Frédéric Bourgeois,Vincent Colin,András Stipsicz
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 50,8 Mb
Release : 2014-03-10
Category : Science
ISBN : 9783319020365
Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
Author : Gerd Fischer,Ulf Rehmann
Publisher : Unknown
Page : 904 pages
File Size : 55,6 Mb
Release : 1998
Category : Mathematics
ISBN : CORNELL:31924085346140
Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 53,5 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author : Ricardo Castaño-Bernard,Yan S. Soibelman,Ilia Zharkov
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 54,7 Mb
Release : 2010
Category : Algebraic varieties
ISBN : 9780821848845
This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. --
Author : Noriko Yui, Helena Verrill, and Charles F. Doran
Publisher : American Mathematical Soc.
Page : 324 pages
File Size : 40,8 Mb
Release : 2024-06-17
Category : Duality (Mathematics)
ISBN : 0821871579
"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 : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer
Page : 210 pages
File Size : 47,6 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540798149
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.
Author : Ron Donagi,Tony Pantev,Dmitry Arinkin
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 53,6 Mb
Release : 2008-04-03
Category : Mathematics
ISBN : 0821866427
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O}^{\times}$ gerbe over a genus one fibration which is a twisted form of $X$. The roles of the gerbe and the twist are interchanged by the authors' duality. The authors state a general conjecture extending this to allow singular fibers, and they prove the conjecture when $X$ is a surface. The duality extends to an action of the full modular group. This duality is related to the Strominger-Yau-Zaslow version of mirror symmetry, to twisted sheaves, and to non-commutative geometry.
