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Gromov-Witten Theory of Spin Curves and Orbifolds

Author: Tyler Jamison Jarvis

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 202

ISBN-13: 0821835343

This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies. A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.

Orbifolds in Mathematics and Physics

Author: Alejandro Adem

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 370

ISBN-13: 0821829904

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This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.

Real and Complex Submanifolds

Author: Young Jin Suh

Publisher: Springer

Published: 2014-12-05

Total Pages: 510

ISBN-13: 4431552154

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Edited in collaboration with the Grassmann Research Group, this book contains many important articles delivered at the ICM 2014 Satellite Conference and the 18th International Workshop on Real and Complex Submanifolds, which was held at the National Institute for Mathematical Sciences, Daejeon, Republic of Korea, August 10–12, 2014. The book covers various aspects of differential geometry focused on submanifolds, symmetric spaces, Riemannian and Lorentzian manifolds, and Kähler and Grassmann manifolds.

Surveys on Recent Developments in Algebraic Geometry

Author: Izzet Coskun

Publisher: American Mathematical Soc.

Published: 2017-07-12

Total Pages: 370

ISBN-13: 1470435578

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The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.

Hilbert Schemes of Points and Infinite Dimensional Lie Algebras

Author: Zhenbo Qin

Publisher: American Mathematical Soc.

Published: 2018-02-26

Total Pages: 336

ISBN-13: 1470441888

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Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes of collections of points (zero-dimensional subschemes) in a smooth algebraic surface . Schemes turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of , including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of and the Gromov–Witten correspondence. The last part of the book presents results about quantum cohomology of and related questions. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.

String-Math 2011

Author: Jonathan Block

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 506

ISBN-13: 0821872958

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The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory and quantum field theory have contributed a series of profound ideas that gave rise to entirely new mathematical fields and revitalized older ones. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. A large and rapidly growing number of both mathematicians and physicists are working at the string-theoretic interface between the two academic fields. The String-Math conference series aims to bring together leading mathematicians and mathematically minded physicists working in this interface. This volume contains the proceedings of the inaugural conference in this series, String-Math 2011, which was held June 6-11, 2011, at the University of Pennsylvania.

Algebraic Geometry

Author: Dan Abramovich

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 506

ISBN-13: 0821847023

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This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.

Regulators

Author: José Ignacio Burgos Gil

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 290

ISBN-13: 0821853228

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This volume contains the proceedings of the Regulators III Conference, held from July 12 to July 22, 2010, in Barcelona, Spain. Regulators can be thought of as realizations from motivic cohomology, which is very difficult to compute, to more computable theories such as Hodge, Betti, l-adic, and Deligne cohomology. It is a very intricate subject that thrives on its interaction with algebraic K-theory, arithmetic geometry, number theory, motivic cohomology, Hodge theory and mathematical physics. The articles in this volume are a reflection of the various approaches to this subject, such as results on motivic cohomology, descriptions of regulators, a revisiting of a number of fundamental conjectures (such as new results pertaining to the Hodge and standard conjectures), and more.

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

Author: Chiu-Chu Melissa Liu

Publisher: American Mathematical Soc.

Published: 2018-11-19

Total Pages: 549

ISBN-13: 1470435411

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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.

Geometric and Topological Methods for Quantum Field Theory

Author: Sylvie Paycha

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 272

ISBN-13: 0821840622

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This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.