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Author: Jonny Evans Publisher: Cambridge University Press ISBN: 1009372661 Category : Mathematics Languages : en Pages : 242
Book Description
Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.
Author: Ron Donagi Publisher: American Mathematical Soc. ISBN: 0821840924 Category : Mathematics Languages : en Pages : 104
Book Description
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 Publisher: Cambridge University Press ISBN: 1108905617 Category : Mathematics Languages : en Pages : 200
Book Description
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: Spiro Karigiannis Publisher: Springer Nature ISBN: 1071605771 Category : Mathematics Languages : en Pages : 392
Book Description
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 Publisher: American Mathematical Soc. ISBN: 9780821821596 Category : Mathematics Languages : en Pages : 392
Book Description
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: Frédéric Bourgeois Publisher: Springer Science & Business Media ISBN: 3319020366 Category : Science Languages : en Pages : 538
Book Description
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: Lotte Hollands Publisher: Amsterdam University Press ISBN: 9085550203 Category : Mathematics Languages : en Pages : 310
Book Description
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: Jonny Evans
Author: Jonny Evans
Author: Jonny Evans
Author: Ron Donagi
Author: M. J. D. Hamilton
Author: Amaury Freslon
Author: Daniel Sanz-Alonso
Author: Spiro Karigiannis
Author: Cumrun Vafa
Author: Frédéric Bourgeois
Author: Lotte Hollands