Non-Kissing Complexes and Tau-Tilting for Gentle Algebras
Author: Yann Palu
Publisher: American Mathematical Society
Published: 2021-12-30
Total Pages: 95
ISBN-13: 1470450046
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Lanterna Rally
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Advances in Representation Theory of Algebras
Author: Ibrahim Assem
Publisher: American Mathematical Soc.
Published: 2021-01-06
Total Pages: 257
ISBN-13: 147045159X
DOWNLOAD EBOOK →The Seventh ARTA (“Advances in Representation Theory of Algebras VII”) conference took place at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México, in Mexico City, from September 24–28, 2018, in honor of José Antonio de la Peña's 60th birthday. Papers in this volume cover topics Professor de la Peña worked on, such as covering theory, tame algebras, and the use of quadratic forms in representation theory. Also included are papers on the categorical approach to representations of algebras and relations to Lie theory, Cohen–Macaulay modules, quantum groups and other algebraic structures.
Handbook of Tilting Theory
Author: Lidia Angeleri Hügel
Publisher: Cambridge University Press
Published: 2007-01-04
Total Pages: 482
ISBN-13: 9780521680455
DOWNLOAD EBOOK →A handbook of key articles providing both an introduction and reference for newcomers and experts alike.
Higher Segal Spaces
Author: Tobias Dyckerhoff
Publisher: Springer Nature
Published: 2019-10-17
Total Pages: 218
ISBN-13: 3030271242
DOWNLOAD EBOOK →This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen’s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.
Extended Abstracts EuroComb 2021
Author: Jaroslav Nešetřil
Publisher: Springer Nature
Published: 2021-08-23
Total Pages: 875
ISBN-13: 3030838234
DOWNLOAD EBOOK →This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.
Introduction to Soergel Bimodules
Author: Ben Elias
Publisher: Springer Nature
Published: 2020-09-26
Total Pages: 588
ISBN-13: 3030488268
DOWNLOAD EBOOK →This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research. This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers.
Discrete Painlevé Equations
Author: Nalini Joshi
Publisher: American Mathematical Soc.
Published: 2019-05-30
Total Pages: 146
ISBN-13: 1470450380
DOWNLOAD EBOOK →Discrete Painlevé equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic geometry, Coxeter groups, topology, special functions theory, and mathematical physics. This book necessarily starts with introductory material to give the reader an accessible entry point to this vast subject matter. It is based on lectures that the author presented as principal lecturer at a Conference Board of Mathematical Sciences and National Science Foundation conference in Texas in 2016. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.
Formal Power Series and Algebraic Combinatorics
Author: Daniel Krob
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 815
ISBN-13: 3662041669
DOWNLOAD EBOOK →This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
Noncommutative Motives
Author: Gonçalo Tabuada
Publisher: American Mathematical Soc.
Published: 2015-09-21
Total Pages: 114
ISBN-13: 1470423979
DOWNLOAD EBOOK →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.
Pseudoperiodic Topology
Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 196
ISBN-13: 9780821820940
DOWNLOAD EBOOK →This volume offers an account of the present state of the art in pseudoperiodic topology--a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors ... have done much to show how modern mathematics begets, from this sea of pathological counterexamples, remarkable general and universal laws, whose discovery would be unthinkable and whose formulation would be impossible in the naive set-theoretical setting."
