Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics
Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics

Author: Pramod M. Achar

Publisher: American Mathematical Society

Published: 2014-08-27

Total Pages: 296

ISBN-13: 0821898523

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This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

Lectures on Algebraic Quantum Groups
Lectures on Algebraic Quantum Groups

Author: Ken Brown

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 339

ISBN-13: 303488205X

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This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Representation Theory and Algebraic Geometry
Representation Theory and Algebraic Geometry

Author: Vladimir Baranovsky

Publisher: Springer Nature

Published: 2022-06-15

Total Pages: 458

ISBN-13: 3030820076

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The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Hodge Theory and Classical Algebraic Geometry
Hodge Theory and Classical Algebraic Geometry

Author: Gary Kennedy

Publisher: American Mathematical Soc.

Published: 2015-08-27

Total Pages: 148

ISBN-13: 1470409909

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This volume contains the proceedings of a conference on Hodge Theory and Classical Algebraic Geometry, held May 13-15, 2013, at The Ohio State University, Columbus, OH. Hodge theory is a powerful tool for the study and classification of algebraic varieties. This volume surveys recent progress in Hodge theory, its generalizations, and applications. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito's theory of mixed Hodge modules, and connections with derived category theory and non-commutative motives.

Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics
Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics

Author: Kailash C. Misra

Publisher: American Mathematical Soc.

Published: 2016-06-28

Total Pages: 370

ISBN-13: 1470418444

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This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography
Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography

Author: Delaram Kahrobaei

Publisher: American Mathematical Soc.

Published: 2015-02-25

Total Pages: 136

ISBN-13: 0821898590

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This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9-10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6-7, 2013 at Boston College, Chestnut Hill, MA. Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.

Geometry, Groups and Dynamics
Geometry, Groups and Dynamics

Author: C. S. Aravinda

Publisher: American Mathematical Soc.

Published: 2015-05-01

Total Pages: 386

ISBN-13: 0821898825

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This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.

Representations of Lie Algebras, Quantum Groups and Related Topics
Representations of Lie Algebras, Quantum Groups and Related Topics

Author: Naihuan Jing

Publisher: American Mathematical Soc.

Published: 2018-08-21

Total Pages: 242

ISBN-13: 1470436965

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This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.

2017 MATRIX Annals
2017 MATRIX Annals

Author: Jan de Gier

Publisher: Springer

Published: 2019-03-13

Total Pages: 702

ISBN-13: 3030041611

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​MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in its second year, 2017: - Hypergeometric Motives and Calabi–Yau Differential Equations - Computational Inverse Problems - Integrability in Low-Dimensional Quantum Systems - Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book - Combinatorics, Statistical Mechanics, and Conformal Field Theory - Mathematics of Risk - Tutte Centenary Retreat - Geometric R-Matrices: from Geometry to Probability The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Geometry and Topology of Submanifolds and Currents
Geometry and Topology of Submanifolds and Currents

Author: Weiping Li

Publisher: American Mathematical Soc.

Published: 2015-08-25

Total Pages: 200

ISBN-13: 1470415569

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he papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.