Recent Progress On The Donaldson Thomas Theory
DOWNLOAD
Download Recent Progress On The Donaldson Thomas Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Recent Progress On The Donaldson Thomas Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Recent Progress On The Donaldson Thomas Theory
DOWNLOAD
Author : Yukinobu Toda
language : en
Publisher: Springer Nature
Release Date : 2021-12-15
Recent Progress On The Donaldson Thomas Theory written by Yukinobu Toda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-15 with Science categories.
This book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten/Donaldson–Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi–Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar–Vafa invariant, which was first proposed by Gopakumar–Vafa in 1998, but its precise mathematical definition has not been available until recently. This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.
Recent Progress On The Donaldson Thomas Theory
DOWNLOAD
Author : Yukinobu Toda
language : en
Publisher:
Release Date : 2021
Recent Progress On The Donaldson Thomas Theory written by Yukinobu Toda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book is an exposition of recent progress on the Donaldson-Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi-Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov-Witten/Donaldson-Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi-Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar-Vafa invariant, which was first proposed by Gopakumar-Vafa in 1998, but its precise mathematical definition has not been available until recently. This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.
Recent Progress In Mathematics
DOWNLOAD
Author : Nam-Gyu Kang
language : en
Publisher: Springer Nature
Release Date : 2022-09-30
Recent Progress In Mathematics written by Nam-Gyu Kang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-30 with Mathematics categories.
This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas. Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson–Thomas theory for Calabi–Yau 4-folds, and Vafa–Witten invariants. Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale–Kato–Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations. Simon Brendle discusses recent developments that have led to a complete classification of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension 3. Hyeonbae Kang reviews some of the developments in the Neumann–Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO. Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit “discriminant-like” affine algebraic varieties.
Surveys On Recent Developments In Algebraic Geometry
DOWNLOAD
Author : Izzet Coskun
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-12
Surveys On Recent Developments In Algebraic Geometry written by Izzet Coskun and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions categories.
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.
Groups Modules And Model Theory Surveys And Recent Developments
DOWNLOAD
Author : Manfred Droste
language : en
Publisher: Springer
Release Date : 2017-06-02
Groups Modules And Model Theory Surveys And Recent Developments written by Manfred Droste and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-02 with Mathematics categories.
This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Frontiers In Differential Geometry Partial Differential Equations And Mathematical Physics
DOWNLOAD
Author : Molin Ge
language : en
Publisher: World Scientific
Release Date : 2014-03-18
Frontiers In Differential Geometry Partial Differential Equations And Mathematical Physics written by Molin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-18 with Science categories.
This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime. All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the frontiers of the related subjects. Contents:A Profile of the Late Professor Gu Chaohao (Tatsien Li)List of Publications of Gu ChaohaoIn Memory of Professor Gu Chaohao (Xiaqi Ding)In Memory of Professor Gu Chaohao (Gongqing Zhang (Kung-Ching Chang))Stability of E-H Mach Configuration in Pseudo-Steady Compressible Flow (Shuxing Chen)Incompressible Viscous Fluid Flows with Slip Boundary Conditions and Their Numerical Simulations (Ben-yu Guo)Global Existence and Uniqueness of the Solution for the Generalized Schrödinger-KdV System (Boling Guo, Bolin Ma & Jingjun Zhang)Anomaly Cancellation and Modularity (Fei Han, Kefeng Liu & Weiping Zhang)On Interior Estimates for Mean Curvature of Convex Surfaces in R3 and Its Applications (Jiaxing Hong)Geometric Invariant Theory of the Space — A Modern Approach to Solid Geometry (Wu-Yi Hsiang)Optimal Convergence Rate of the Binomial Tree Scheme for American Options and Their Free Boundaries (Lishang Jiang & Jin Liang)Rademacher Φ Function, Jacobi Symbols, Quantum and Classical Invariants of Lens Spaces (Bang-He Li & Tian-Jun Li)Historical Review on the Roles of Mathematics in the Study of Aerodynamics (Jiachun Li)Toward Chern–Simons Theory of Complexes on Calabi–Yau Threefolds (Jun Li)Exact Boundary Synchronization for a Coupled System of Wave Equations (Tatsien Li)Scaling Limit for Compressible Viscoelastic Fluids (Xianpeng Hu & Fang-Hua Lin)Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds (Ngaiming Mok)The Application of Conditional Nonlinear Optimal Perturbation to Targeted Observations for Tropical Cyclone Prediction (Mu Mu, Feifan Zhou, Xiaohao Qin & Boyu Chen)Isometric Immersions in Minkowski Spaces (Yi-Bing Shen)Remarks on Volume Growth for Minimal Graphs in Higher Codimension (Yuanlong Xin)Separation of Variables for the Lax Pair of the Bogomolny Equation in 2+1 Dimensional Anti-de Sitter Space-Time (Zi-Xiang Zhou) Readership: Mathematicians and advanced graduate students in mathematics. Key Features:In memory of the highly distinguished mathematician Gu ChaohaoThe contributors are excellent experts, including 9 members of the CASProvides some important information on Differential Geometry, Partial Differential Equations, Mathematical Physics, etcKeywords:Differential Geometry;Partial Differential Equations;Mathematical Physics
Moduli Spaces
DOWNLOAD
Author : Leticia Brambila
language : en
Publisher: Cambridge University Press
Release Date : 2014-03-13
Moduli Spaces written by Leticia Brambila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-13 with Mathematics categories.
A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.
String Math 2022
DOWNLOAD
Author : Ron Donagi
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-18
String Math 2022 written by Ron Donagi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.
This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.
String Math 2014
DOWNLOAD
Author : Vincent Bouchard:
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-10
String Math 2014 written by Vincent Bouchard: and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-10 with $K$-theory categories.
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.
Representation Theory And Beyond
DOWNLOAD
Author : Jan Šťovíček
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-11-13
Representation Theory And Beyond written by Jan Šťovíček and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with Education categories.
This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.