Expository Lectures On Representation Theory

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Expository Lectures on Representation Theory

Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov
Expository Lectures on Representation Theory Book PDF

Author : Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 52,8 Mb
Release : 2014-01-16
Category : Mathematics
ISBN : 9780821891407

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Expository Lectures on Representation Theory by Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov Pdf

This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2012, in Falmouth, MA. The representation theory of finite dimensional algebras and related topics, especially cluster combinatorics, is a very active topic of research. This volume contains papers covering both the history and the latest developments in this topic. In particular, Otto Kerner gives a review of basic theorems and latest results about wild hereditary algebras, Yuri Berest develops the theory of derived representation schemes, and Markus Schmidmeier presents new applications of arc diagrams.

Lectures on Representation Theory

Jing-Song Huang
Lectures on Representation Theory Book PDF

Author : Jing-Song Huang
Publisher : World Scientific
Page : 206 pages
File Size : 51,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9810237251

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Lectures on Representation Theory by Jing-Song Huang Pdf

This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.

Perspectives in Representation Theory

Pavel Etingof,Mikhail Khovanov,Alistair Savage
Perspectives in Representation Theory Book PDF

Author : Pavel Etingof,Mikhail Khovanov,Alistair Savage
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 55,7 Mb
Release : 2014-03-11
Category : Mathematics
ISBN : 9780821891704

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Perspectives in Representation Theory by Pavel Etingof,Mikhail Khovanov,Alistair Savage Pdf

This volume contains the proceedings of the conference Perspectives in Representation Theory, held from May 12-17, 2012, at Yale University, in honor of Igor Frenkel's 60th birthday. The aim of the conference was to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands program, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and -adic groups, and quantum gauge theories. The papers in this volume present representation theory connections to numerous other subjects, as well as some of the most recent advances in representation theory, including those which occurred thanks to the application of techniques in other areas of mathematics, and of ideas of quantum field theory and string theory.

Geometric and Topological Aspects of the Representation Theory of Finite Groups

Jon F. Carlson,Srikanth B. Iyengar,Julia Pevtsova
Geometric and Topological Aspects of the Representation Theory of Finite Groups Book PDF

Author : Jon F. Carlson,Srikanth B. Iyengar,Julia Pevtsova
Publisher : Springer
Page : 493 pages
File Size : 42,8 Mb
Release : 2018-10-04
Category : Mathematics
ISBN : 9783319940335

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Geometric and Topological Aspects of the Representation Theory of Finite Groups by Jon F. Carlson,Srikanth B. Iyengar,Julia Pevtsova Pdf

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

Topology and Representation Theory

Eric M. Friedlander,Mark E. Mahowald,American Mathematical Society
Topology and Representation Theory Book PDF

Author : Eric M. Friedlander,Mark E. Mahowald,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 51,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851654

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Topology and Representation Theory by Eric M. Friedlander,Mark E. Mahowald,American Mathematical Society Pdf

During 1991-1992, Northwestern University conducted a special emphasis year on the topic, 'The connections between topology and representation theory'. Activities over the year culminated in a conference in May 1992 which attracted over 120 participants. Most of the plenary lectures at the conference were expository and designed to introduce current trends to graduate students and nonspecialists familiar with algebraic topology. This volume contains refereed papers presented or solicited at the conference; one paper is based on a seminar given during the emphasis year.

Recent Developments in Representation Theory

Alex Martsinkovsky,Gordana Todorov,Kiyoshi Igusa
Recent Developments in Representation Theory Book PDF

Author : Alex Martsinkovsky,Gordana Todorov,Kiyoshi Igusa
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 48,6 Mb
Release : 2016-08-26
Category : Associative rings
ISBN : 9781470419554

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Recent Developments in Representation Theory by Alex Martsinkovsky,Gordana Todorov,Kiyoshi Igusa Pdf

This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1–6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.

Representations of Algebras

Graham J. Leuschke,Frauke Bleher,Ralf Schiffler,Dan Zacharia
Representations of Algebras Book PDF

Author : Graham J. Leuschke,Frauke Bleher,Ralf Schiffler,Dan Zacharia
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 49,9 Mb
Release : 2018
Category : Algebra
ISBN : 9781470435769

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Representations of Algebras by Graham J. Leuschke,Frauke Bleher,Ralf Schiffler,Dan Zacharia Pdf

This volume contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held from August 10-19, 2016, at Syracuse University, Syracuse, NY. Included are three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories. Other articles represent contributions to areas in and related to representation theory, such as noncommutative resolutions, twisted commutative algebras, and upper cluster algebras.

Surveys in Representation Theory of Algebras

Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov
Surveys in Representation Theory of Algebras Book PDF

Author : Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 43,6 Mb
Release : 2018-09-12
Category : Representations of algebras
ISBN : 9781470436797

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Surveys in Representation Theory of Algebras by Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov Pdf

This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.

Ring Theory and Its Applications

Dinh Van Huynh, S. K. Jain, Sergio R. López-Permouth,S. Tariq Rizvi,Cosmin S. Roman
Ring Theory and Its Applications Book PDF

Author : Dinh Van Huynh, S. K. Jain, Sergio R. López-Permouth,S. Tariq Rizvi,Cosmin S. Roman
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 52,7 Mb
Release : 2014-02-21
Category : Mathematics
ISBN : 9780821887974

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Ring Theory and Its Applications by Dinh Van Huynh, S. K. Jain, Sergio R. López-Permouth,S. Tariq Rizvi,Cosmin S. Roman Pdf

This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.

Operator Methods in Wavelets, Tilings, and Frames

Keri A. Kornelson,Eric S. Weber
Operator Methods in Wavelets Tilings and Frames Book PDF

Author : Keri A. Kornelson,Eric S. Weber
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 45,5 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9781470410407

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Operator Methods in Wavelets, Tilings, and Frames by Keri A. Kornelson,Eric S. Weber Pdf

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings, held April 13-14, 2013, in Boulder, Colorado. Frames were first introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series but have enjoyed widespread interest in recent years, particularly as a unifying concept. Indeed, mathematicians with backgrounds as diverse as classical and modern harmonic analysis, Banach space theory, operator algebras, and complex analysis have recently worked in frame theory. Frame theory appears in the context of wavelets, spectra and tilings, sampling theory, and more. The papers in this volume touch on a wide variety of topics, including: convex geometry, direct integral decompositions, Beurling density, operator-valued measures, and splines. These varied topics arise naturally in the study of frames in finite and infinite dimensions. In nearly all of the papers, techniques from operator theory serve as crucial tools to solving problems in frame theory. This volume will be of interest not only to researchers in frame theory but also to those in approximation theory, representation theory, functional analysis, and harmonic analysis.

Discrete Geometry and Algebraic Combinatorics

Alexander Barg,Oleg R. Musin
Discrete Geometry and Algebraic Combinatorics Book PDF

Author : Alexander Barg,Oleg R. Musin
Publisher : American Mathematical Society
Page : 202 pages
File Size : 54,5 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9781470409050

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Discrete Geometry and Algebraic Combinatorics by Alexander Barg,Oleg R. Musin Pdf

This volume contains the proceedings of the AMS Special Session on Discrete Geometry and Algebraic Combinatorics held on January 11, 2013, in San Diego, California. The collection of articles in this volume is devoted to packings of metric spaces and related questions, and contains new results as well as surveys of some areas of discrete geometry. This volume consists of papers on combinatorics of transportation polytopes, including results on the diameter of graphs of such polytopes; the generalized Steiner problem and related topics of the minimal fillings theory; a survey of distance graphs and graphs of diameters, and a group of papers on applications of algebraic combinatorics to packings of metric spaces including sphere packings and topics in coding theory. In particular, this volume presents a new approach to duality in sphere packing based on the Poisson summation formula, applications of semidefinite programming to spherical codes and equiangular lines, new results in list decoding of a family of algebraic codes, and constructions of bent and semi-bent functions.

Biological Fluid Dynamics: Modeling, Computations, and Applications

Anita T. Layton, Sarah D. Olson
Biological Fluid Dynamics Modeling Computations and Applications Book PDF

Author : Anita T. Layton, Sarah D. Olson
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 47,6 Mb
Release : 2014-10-14
Category : Mathematics
ISBN : 9780821898505

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Biological Fluid Dynamics: Modeling, Computations, and Applications by Anita T. Layton, Sarah D. Olson Pdf

This volume contains the Proceedings of the AMS Special Session on Biological Fluid Dynamics: Modeling, Computation, and Applications, held on October 13, 2012, at Tulane University, New Orleans, Louisiana. In recent years, there has been increasing interest in the development and application of advanced computational techniques for simulating fluid motion driven by immersed flexible structures. That interest is motivated, in large part, by the multitude of applications in physiology and biology. In some biological systems, fluid motion is driven by active biological tissues, which are typically constructed of fibers that are surrounded by fluid. Not only do the fibers hold the tissues together, they also transmit forces that ultimately result in fluid motion. In other examples, the fluid may flow through conduits such as blood vessels or airways that are flexible or active. That is, those conduits may react to and affect the fluid dynamics. This volume responds to the widespread interest among mathematicians, biologists, and engineers in fluid-structure interactions problems. Included are expository and review articles in biological fluid dynamics. Applications that are considered include ciliary motion, upside-down jellyfish, biological feedback in the kidney, peristalsis and dynamic suction pumping, and platelet cohesion and adhesion.

Algebraic Topology: Applications and New Directions

Ulrike Tillmann, Søren Galatius, Dev Sinha
Algebraic Topology Applications and New Directions Book PDF

Author : Ulrike Tillmann, Søren Galatius, Dev Sinha
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 54,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9780821894743

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Algebraic Topology: Applications and New Directions by Ulrike Tillmann, Søren Galatius, Dev Sinha Pdf

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.

The Influence of Solomon Lefschetz in Geometry and Topology

Ernesto Lupercio, Francisco J. Turrubiates
The Influence of Solomon Lefschetz in Geometry and Topology Book PDF

Author : Ernesto Lupercio, Francisco J. Turrubiates
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 47,9 Mb
Release : 2014-08-05
Category : Mathematics
ISBN : 9780821894941

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The Influence of Solomon Lefschetz in Geometry and Topology by Ernesto Lupercio, Francisco J. Turrubiates Pdf

The influence of Solomon Lefschetz (1884-1972) in geometry and topology 40 years after his death has been very profound. Lefschetz's influence in Mexican mathematics has been even greater. In this volume, celebrating 50 years of mathematics at Cinvestav-México, many of the fields of geometry and topology are represented by some of the leaders of their respective fields. This volume opens with Michael Atiyah reminiscing about his encounters with Lefschetz and México. Topics covered in this volume include symplectic flexibility, Chern-Simons theory and the theory of classical theta functions, toric topology, the Beilinson conjecture for finite-dimensional associative algebras, partial monoids and Dold-Thom functors, the weak b-principle, orbit configuration spaces, equivariant extensions of differential forms for noncompact Lie groups, dynamical systems and categories, and the Nahm pole boundary condition.

Hodge Theory, Complex Geometry, and Representation Theory

Mark Green, Phillip Griffiths,Matt Kerr
Hodge Theory Complex Geometry and Representation Theory Book PDF

Author : Mark Green, Phillip Griffiths,Matt Kerr
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 54,5 Mb
Release : 2013-11-05
Category : Mathematics
ISBN : 9781470410124

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Hodge Theory, Complex Geometry, and Representation Theory by Mark Green, Phillip Griffiths,Matt Kerr Pdf

This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.