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Perspectives in Representation Theory

Author: Pavel Etingof

Publisher: American Mathematical Soc.

Published: 2014-03-11

Total Pages: 384

ISBN-13: 0821891707

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.

Algebraic and Analytic Methods in Representation Theory

Author:

Publisher: Elsevier

Published: 1996-09-27

Total Pages: 357

ISBN-13: 0080526950

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This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike. Presents several different points of view on key topics in representation theory, from internationally known experts in the field

Representation Theory -- Current Trends and Perspectives

Author: Henning Krause

Publisher:

Published: 2017

Total Pages: 0

ISBN-13: 9783037191712

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From April 2009 until March 2016, the German Science Foundation generously supported the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, which are also reflected in the contributions to this volume. Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles. This volume covers current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras, and of infinite dimensional Lie groups. Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject.

Persistence Theory: From Quiver Representations to Data Analysis

Author: Steve Y. Oudot

Publisher: American Mathematical Soc.

Published: 2017-05-17

Total Pages: 229

ISBN-13: 1470434431

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Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Perspectives of Representation Theory and Noncommutative Harmonic Analysis

Author:

Publisher:

Published: 2013

Total Pages: 204

ISBN-13:

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Representation Theory, Mathematical Physics, and Integrable Systems

Author: Anton Alekseev

Publisher: Springer Nature

Published: 2022-02-05

Total Pages: 652

ISBN-13: 3030781488

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Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

Author: Pavel I. Etingof

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 215

ISBN-13: 0821804960

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This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.

Perspectives in Lie Theory

Author: Filippo Callegaro

Publisher: Springer

Published: 2017-12-07

Total Pages: 461

ISBN-13: 3319589717

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Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Handbook of Learning from Multiple Representations and Perspectives

Author: Peggy Van Meter

Publisher: Routledge

Published: 2020-03-10

Total Pages: 696

ISBN-13: 0429813651

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In and out of formal schooling, online and off, today’s learners must consume and integrate a level of information that is exponentially larger and delivered through a wider range of formats and viewpoints than ever before. The Handbook of Learning from Multiple Representations and Perspectives provides a path for understanding the cognitive, motivational, and socioemotional processes and skills necessary for learners across educational contexts to make sense of and use information sourced from varying inputs. Uniting research and theory from education, psychology, literacy, library sciences, media and technology, and more, this forward-thinking volume explores the common concerns, shared challenges, and thematic patterns in our capacity to make meaning in an information-rich society. Chapter 16 of this book is freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com/books/e/9780429443961.

Perspectives on Mental Representation

Author: Jacques Mehler

Publisher: Routledge

Published: 2017-03-16

Total Pages: 478

ISBN-13: 1315521911

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Originally published in 1982, the editors felt that their field was clearly in need of explanatory accounts for many different areas. This volume presents statements of the status of research in several areas by scholars at the forefront of the discipline. It tries at the same time to juxtapose theoretical and experimental perspectives in order to display some of the major lines of tension in the field. Divided into 5 parts it covers: Theoretical Perspectives; Experimental Studies in Processing; Neuropsychological Studies in Processing; Studies in Development; followed by Commentary on some specific chapters.