Expository Lectures on Representation Theory

Expository Lectures on Representation Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 236
Release :
ISBN-10 : 9780821891407
ISBN-13 : 0821891405
Rating : 4/5 (07 Downloads)

Synopsis Expository Lectures on Representation Theory by : Kiyoshi Igusa

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.

Introduction to Representation Theory

Introduction to Representation Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 240
Release :
ISBN-10 : 9780821853511
ISBN-13 : 0821853511
Rating : 4/5 (11 Downloads)

Synopsis Introduction to Representation Theory by : Pavel I. Etingof

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Recent Developments in Representation Theory

Recent Developments in Representation Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 258
Release :
ISBN-10 : 9781470419554
ISBN-13 : 1470419556
Rating : 4/5 (54 Downloads)

Synopsis Recent Developments in Representation Theory by : Alex Martsinkovsky

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.

Surveys in Representation Theory of Algebras

Surveys in Representation Theory of Algebras
Author :
Publisher : American Mathematical Soc.
Total Pages : 216
Release :
ISBN-10 : 9781470436797
ISBN-13 : 1470436795
Rating : 4/5 (97 Downloads)

Synopsis Surveys in Representation Theory of Algebras by : Alex Martsinkovsky

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.

Representations of Algebras

Representations of Algebras
Author :
Publisher : American Mathematical Soc.
Total Pages : 294
Release :
ISBN-10 : 9781470435769
ISBN-13 : 1470435764
Rating : 4/5 (69 Downloads)

Synopsis Representations of Algebras by : Graham J. Leuschke

Contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held in August 2016, at Syracuse University. This volume includes 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.

Ring Theory and Its Applications

Ring Theory and Its Applications
Author :
Publisher : American Mathematical Soc.
Total Pages : 330
Release :
ISBN-10 : 9780821887974
ISBN-13 : 0821887971
Rating : 4/5 (74 Downloads)

Synopsis Ring Theory and Its Applications by : Dinh Van Huynh

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

Operator Methods in Wavelets, Tilings, and Frames
Author :
Publisher : American Mathematical Soc.
Total Pages : 192
Release :
ISBN-10 : 9781470410407
ISBN-13 : 1470410400
Rating : 4/5 (07 Downloads)

Synopsis Operator Methods in Wavelets, Tilings, and Frames by : Keri A. Kornelson

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

Discrete Geometry and Algebraic Combinatorics
Author :
Publisher : American Mathematical Society
Total Pages : 202
Release :
ISBN-10 : 9781470409050
ISBN-13 : 1470409054
Rating : 4/5 (50 Downloads)

Synopsis Discrete Geometry and Algebraic Combinatorics by : Alexander Barg

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

Biological Fluid Dynamics: Modeling, Computations, and Applications
Author :
Publisher : American Mathematical Soc.
Total Pages : 250
Release :
ISBN-10 : 9780821898505
ISBN-13 : 0821898507
Rating : 4/5 (05 Downloads)

Synopsis Biological Fluid Dynamics: Modeling, Computations, and Applications by : Anita T. Layton

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

Algebraic Topology: Applications and New Directions
Author :
Publisher : American Mathematical Soc.
Total Pages : 350
Release :
ISBN-10 : 9780821894743
ISBN-13 : 0821894749
Rating : 4/5 (43 Downloads)

Synopsis Algebraic Topology: Applications and New Directions by : Ulrike Tillmann

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.