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Author : Cheol-Hyun Cho,Hansol Hong,Siu-Cheong Lau
Publisher : American Mathematical Society
Page : 116 pages
File Size : 46,6 Mb
Release : 2021-09-24
Category : Mathematics
ISBN : 9781470447618
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Author : Raf Bocklandt
Publisher : Cambridge University Press
Page : 403 pages
File Size : 48,9 Mb
Release : 2021-08-19
Category : Mathematics
ISBN : 9781108483506
Introduction to homological mirror symmetry from the point of view of representation theory, suitable for graduate students.
Author : Si Li,Bong H. Lian, Wei Song,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 48,9 Mb
Release : 2017-11-28
Category : Algebraic geometry -- Projective and enumerative geometry -- Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
ISBN : 9781470429515
This volume contains the proceedings of the conference String-Math 2015, which was held from December 31, 2015–January 4, 2016, at Tsinghua Sanya International Mathematics Forum in Sanya, China. Two of the main themes of this volume are frontier research on Calabi-Yau manifolds and mirror symmetry and the development of non-perturbative methods in supersymmetric gauge theories. The articles present state-of-the-art developments in these topics. String theory is a broad subject, which has profound connections with broad branches of modern mathematics. In the last decades, the prosperous interaction built upon the joint efforts from both mathematicians and physicists has given rise to marvelous deep results in supersymmetric gauge theory, topological string, M-theory and duality on the physics side, as well as in algebraic geometry, differential geometry, algebraic topology, representation theory and number theory on the mathematics side.
Author : Yong-Geun Oh
Publisher : Springer Nature
Page : 426 pages
File Size : 44,8 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789819717989
Author : Anton Kapustin,Maximilian Kreuzer,Karl-Georg Schlesinger
Publisher : Springer
Page : 272 pages
File Size : 46,6 Mb
Release : 2008-12-15
Category : Science
ISBN : 9783540680307
Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory.
Author : Guillermo Cortiñas
Publisher : American Mathematical Soc.
Page : 289 pages
File Size : 55,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821868645
Luis Santalo Winter Schools are organized yearly by the Mathematics Department and the Santalo Mathematical Research Institute of the School of Exact and Natural Sciences of the University of Buenos Aires (FCEN). This volume contains the proceedings of the third Luis Santalo Winter School which was devoted to noncommutative geometry and held at FCEN July 26-August 6, 2010. Topics in this volume concern noncommutative geometry in a broad sense, encompassing various mathematical and physical theories that incorporate geometric ideas to the study of noncommutative phenomena. It explores connections with several areas including algebra, analysis, geometry, topology and mathematical physics. Bursztyn and Waldmann discuss the classification of star products of Poisson structures up to Morita equivalence. Tsygan explains the connections between Kontsevich's formality theorem, noncommutative calculus, operads and index theory. Hoefel presents a concrete elementary construction in operad theory. Meyer introduces the subject of $\mathrm{C}^*$-algebraic crossed products. Rosenberg introduces Kasparov's $KK$-theory and noncommutative tori and includes a discussion of the Baum-Connes conjecture for $K$-theory of crossed products, among other topics. Lafont, Ortiz, and Sanchez-Garcia carry out a concrete computation in connection with the Baum-Connes conjecture. Zuk presents some remarkable groups produced by finite automata. Mesland discusses spectral triples and the Kasparov product in $KK$-theory. Trinchero explores the connections between Connes' noncommutative geometry and quantum field theory. Karoubi demonstrates a construction of twisted $K$-theory by means of twisted bundles. Tabuada surveys the theory of noncommutative motives.
Author : Anton Kapustin,Maximilian Kreuzer,Karl-Georg Schlesinger
Publisher : Springer
Page : 272 pages
File Size : 45,8 Mb
Release : 2009-08-29
Category : Science
ISBN : 3540863745
Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory.
Author : Gonçalo Tabuada
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 50,7 Mb
Release : 2015-09-21
Category : Algebraic varieties
ISBN : 9781470423971
The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.
Author : M. Hazewinkel
Publisher : Elsevier
Page : 577 pages
File Size : 48,6 Mb
Release : 2008-03-06
Category : Mathematics
ISBN : 9780080564999
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes
Author : Michael Hitrik,Dmitry Tamarkin,Boris Tsygan,Steve Zelditch
Publisher : Springer
Page : 654 pages
File Size : 47,8 Mb
Release : 2018-12-19
Category : Mathematics
ISBN : 9783030015886
This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.
Author : Anton Kapustin,Maximilian Kreuzer
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 50,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9783540680291
An ideal reference on the mathematical aspects of quantum field theory, this volume provides a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives.
Author : Ron Donagi, Michael R. Douglas,Ljudmila Kamenova,Martin Rocek
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 52,5 Mb
Release : 2014-12-02
Category : Mathematics
ISBN : 9781470410513
This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.
Author : Ulrike Tillmann, Søren Galatius, Dev Sinha
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 44,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9780821894743
This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23-27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject. The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic -theory and the theory of operads.
Author : Anonim
Publisher : American Mathematical Soc.
Page : 698 pages
File Size : 45,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821838488
Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.
Author : Anonim
Publisher : World Scientific
Page : 1191 pages
File Size : 43,8 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX