Download or read book Fukaya Categories and Picard Lefschetz Theory written by Paul Seidel and published by European Mathematical Society. This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.
Download or read book Algebra Geometry and Physics in the 21st Century written by Denis Auroux and published by Birkhäuser. This book was released on 2017-07-27 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren
Download or read book Bordered Heegaard Floer Homology written by Robert Lipshitz and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.
Download or read book Homological Mirror Symmetry and Tropical Geometry written by Ricardo Castano-Bernard and published by Springer. This book was released on 2014-10-07 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Contact and Symplectic Topology written by Frédéric Bourgeois and published by Springer Science & Business Media. This book was released on 2014-03-10 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Gentle Introduction to Homological Mirror Symmetry written by Raf Bocklandt and published by Cambridge University Press. This book was released on 2021-08-19 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to homological mirror symmetry from the point of view of representation theory, suitable for graduate students.
Download or read book Lectures on Factorization Homology Categories and Topological Field Theories written by Hiro Lee Tanaka and published by Springer Nature. This book was released on 2020-12-14 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.
Download or read book Lagrangian Intersection Floer Theory written by Kenji Fukaya and published by American Mathematical Soc.. This book was released on 2010-06-21 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.
Download or read book Symplectic Topology and Floer Homology written by Yong-Geun Oh and published by Cambridge University Press. This book was released on 2015-08-27 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second part of a two-volume set offering a systematic explanation of symplectic topology. This volume provides a comprehensive introduction to Hamiltonian and Lagrangian Floer theory.
Download or read book Symplectic Topology and Floer Homology Volume 1 Symplectic Geometry and Pseudoholomorphic Curves written by Yong-Geun Oh and published by Cambridge University Press. This book was released on 2015-08-27 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
Download or read book Symplectic Topology and Floer Homology Volume 2 Floer Homology and its Applications written by Yong-Geun Oh and published by Cambridge University Press. This book was released on 2015-08-27 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. The first volume covered the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.
Download or read book Lagrangian Floer Theory and Its Deformations written by Yong-Geun Oh and published by Springer Nature. This book was released on with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Derived Categories written by Amnon Yekutieli and published by Cambridge University Press. This book was released on 2019-12-19 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been remarkably few systematic expositions of the theory of derived categories since its inception in the work of Grothendieck and Verdier in the 1960s. This book is the first in-depth treatment of this important component of homological algebra. It carefully explains the foundations in detail before moving on to key applications in commutative and noncommutative algebra, many otherwise unavailable outside of research articles. These include commutative and noncommutative dualizing complexes, perfect DG modules, and tilting DG bimodules. Written with graduate students in mind, the emphasis here is on explicit constructions (with many examples and exercises) as opposed to axiomatics, with the goal of demystifying this difficult subject. Beyond serving as a thorough introduction for students, it will serve as an important reference for researchers in algebra, geometry and mathematical physics.
Download or read book String Math 2022 written by Ron Donagi and published by American Mathematical Society. This book was released on 2024-04-18 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Floer Cohomology and Flips written by François Charest and published by American Mathematical Society. This book was released on 2022-08-31 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Mexican Mathematicians Abroad written by Noé Bárcenas and published by American Mathematical Soc.. This book was released on 2016-02-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the First Workshop “Matemáticos Mexicanos Jóvenes en el Mundo”, held from August 22–24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. - See more at: http://bookstore.ams.org/conm-657/#sthash.cUjwTcvX.dpuf This volume contains the proceedings of the First Workshop "Matemáticos Mexicanos Jóvenes en el Mundo", held from August 22-24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. One of the main goals of this meeting was to present different research directions being pursued by young Mexican mathematicians based in other countries, such as Brazil, Canada, Colombia, Estonia, Germany, Spain and the United States, showcasing research lines currently underrepresented in Mexico. Featured are survey and research articles in six areas: algebra, analysis, applied mathematics, geometry, probability and topology. Their topics range from current developments related to well-known open problems to novel interactions between pure mathematics and computer science. Most of the articles provide a panoramic view of the fields and problems the authors work on, making the book accessible to advanced graduate students and researchers in mathematics from different fields. This book is published in cooperation with Sociedad Matemática Mexicana.
Download or read book Trends in Representation Theory of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.