Gromov-Witten Theory and Spectral Curve Topological Recursion PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Gromov-Witten Theory and Spectral Curve Topological Recursion PDF full book. Access full book title Gromov-Witten Theory and Spectral Curve Topological Recursion by . Download full books in PDF and EPUB format.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 156
Get Book Here
Book Description
"Gromov-Witten theory and spectral curve topological recursion are important parts of modern algebraic geometry and mathematical physics. In my thesis I study relations between these theories and some important new aspects and applications of them. In particular, a construction for a local spectral curve which produces the same invariants as a given Gromov-Witten theory is presented in the thesis, as well as constructions for quantum spectral curves for several important theories, and a new proof of the so-called ELSV formula."--Samenvatting auteur.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 156
Get Book Here
Book Description
"Gromov-Witten theory and spectral curve topological recursion are important parts of modern algebraic geometry and mathematical physics. In my thesis I study relations between these theories and some important new aspects and applications of them. In particular, a construction for a local spectral curve which produces the same invariants as a given Gromov-Witten theory is presented in the thesis, as well as constructions for quantum spectral curves for several important theories, and a new proof of the so-called ELSV formula."--Samenvatting auteur.
Author: Quinten Weller
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 0
Get Book Here
Book Description
The topological recursion is a construction in algebraic geometry that takes in the data of a so-called spectral curve, $\mathcal{S}=\left(\Sigma,x,y\right)$ where $\Sigma$ is a Riemann surface and $x,y:\Sigma\to\mathbb{C}_\infty$ are meromorphic, and recursively constructs correlators which, in applications, are then interpreted as generating functions. In many of these applications, for example the $r$-spin Hurwitz case $\mathcal{S}=\left(\mathbb{C},x(z)=z{\rm e}^{-z^r},y(z)={\rm e}^{z^r}\right)$, $x$ has essential singularities when the underlying Riemann surface is compactified. Previously, these essential singularities have been ignored and the topological recursion considered on the non-compact surface. Here we argue that it is more natural to include the essential singularities as ramification points and give the corresponding definition for topological recursion; that is, a topological recursion for \emph{transalgebraic} spectral curves rather than \emph{algebraic} spectral curves. We use this definition to shed light on the TR/QC connection, Hurwitz theory, the Gromov-Witten invariants of $\mathbb{CP}^1$, and mirror curves.
Author: Chiu-Chu Melissa Liu
Publisher: American Mathematical Soc.
ISBN: 1470435411
Category : Topology
Languages : en
Pages : 549
Get Book Here
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: Emily Clader
Publisher: Springer
ISBN: 3319942204
Category : Mathematics
Languages : en
Pages : 625
Get Book Here
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: Richard Wentworth
Publisher: World Scientific
ISBN: 9813229101
Category : Mathematics
Languages : en
Pages : 412
Get Book Here
Book Description
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.
Author: Anton Dzhamay
Publisher: American Mathematical Soc.
ISBN: 0821887475
Category : Mathematics
Languages : en
Pages : 363
Get Book Here
Book Description
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
Author: Renzo Cavalieri
Publisher: Cambridge University Press
ISBN: 1316798933
Category : Mathematics
Languages : en
Pages : 197
Get Book Here
Book Description
Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Author: Piotr Kielanowski
Publisher: Springer Science & Business Media
ISBN: 3034806450
Category : Mathematics
Languages : en
Pages : 237
Get Book Here
Book Description
The Białowieża workshops on Geometric Methods in Physics, taking place in the unique environment of the Białowieża natural forest in Poland, are among the important meetings in the field. Every year some 80 to 100 participants both from mathematics and physics join to discuss new developments and to interchange ideas. The current volume was produced on the occasion of the XXXI meeting in 2012. For the first time the workshop was followed by a School on Geometry and Physics, which consisted of advanced lectures for graduate students and young researchers. Selected speakers of the workshop were asked to contribute, and additional review articles were added. The selection shows that despite its now long tradition the workshop remains always at the cutting edge of ongoing research. The XXXI workshop had as a special topic the works of the late Boris Vasilievich Fedosov (1938–2011) who is best known for a simple and very natural construction of a deformation quantization for any symplectic manifold, and for his contributions to index theory.
Author: Vincent Bouchard:
Publisher: American Mathematical Soc.
ISBN: 1470419920
Category : Mathematics
Languages : en
Pages : 418
Get Book Here
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: Ricardo Castano-Bernard
Publisher: Springer
ISBN: 3319065149
Category : Mathematics
Languages : en
Pages : 445
Get Book Here
Book Description
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.
