Computational Aspects Of Discrete Subgroups Of Lie Groups

Author : Alla Detinko,Michael Kapovich,Alex Kontorovich,Peter Sarnak,Richard Schwartz
Publisher : American Mathematical Society
Page : 164 pages
File Size : 43,7 Mb
Release : 2023-03-10
Category : Mathematics
ISBN : 9781470468040

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Computational Aspects of Discrete Subgroups of Lie Groups by Alla Detinko,Michael Kapovich,Alex Kontorovich,Peter Sarnak,Richard Schwartz Pdf

This volume contains the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held from June 14 to June 18, 2021, and hosted by the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representation of groups and their geometric properties. It is centered on computing with discrete subgroups of Lie groups, which impacts many different areas of mathematics such as algebra, geometry, topology, and number theory. The workshop aimed to synergize independent strands in the area of computing with discrete subgroups of Lie groups, to facilitate solution of theoretical problems by means of recent advances in computational algebra.

Author : Madabusi S. Raghunathan
Publisher : Springer
Page : 230 pages
File Size : 52,8 Mb
Release : 1972-11-16
Category : Mathematics
ISBN : 3540057498

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Discrete Subgroups of Lie Groups by Madabusi S. Raghunathan Pdf

This book originated from a course of lectures given at Yale University during 1968-69 and a more elaborate one, the next year, at the Tata Institute of Fundamental Research. Its aim is to present a detailed ac count of some of the recent work on the geometric aspects of the theory of discrete subgroups of Lie groups. Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous space GJ H carries a finite G-invariant measure). It is assumed that the reader has considerable familiarity with Lie groups and algebraic groups. However most of the results used frequently in the book are summarised in "Preliminaries"; this chapter, it is hoped, will be useful as a reference. We now briefly outline the contents of the book. Chapter I deals with results of a general nature on lattices in locally compact groups. The second chapter is an account of the fairly complete study of lattices in nilpotent Lie groups carried out by Ma1cev. Chapters III and IV are devoted to lattices in solvable Lie groups; most of the theorems here are due to Mostow. In Chapter V we prove a density theorem due to Borel: this is the first important result on lattices in semisimple Lie groups.

Author : Gregori Aleksandrovitsch Margulis
Publisher : Springer
Page : 408 pages
File Size : 50,9 Mb
Release : 1991
Category : Lattice theory
ISBN : UCSC:32106009513067

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Discrete Subgroups of Semisimple Lie Groups by Gregori Aleksandrovitsch Margulis Pdf

Author : Gregori A. Margulis
Publisher : Springer
Page : 0 pages
File Size : 42,7 Mb
Release : 1991-03-01
Category : Mathematics
ISBN : 3642514456

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Discrete Subgroups of Semisimple Lie Groups by Gregori A. Margulis Pdf

A detailed treatment of the geometric aspects of discrete groups was carried out by Raghunathan in his book "Discrete subgroups of Lie Groups" which appeared in 1972. In particular he covered the theory of lattices in nilpotent and solvable Lie groups, results of Mal'cev and Mostow, and proved the Borel density theorem and local rigidity theorem ofSelberg-Weil. He also included some results on unipotent elements of discrete subgroups as well as on the structure of fundamental domains. The chapters concerning discrete subgroups of semi simple Lie groups are essentially concerned with results which were obtained in the 1960's. The present book is devoted to lattices, i.e. discrete subgroups of finite covolume, in semi-simple Lie groups. By "Lie groups" we not only mean real Lie groups, but also the sets of k-rational points of algebraic groups over local fields k and their direct products. Our results can be applied to the theory of algebraic groups over global fields. For example, we prove what is in some sense the best possible classification of "abstract" homomorphisms of semi-simple algebraic group over global fields.

Author : Mee Seong Im,Bach Nguyen,Arik Wilbert
Publisher : American Mathematical Society
Page : 240 pages
File Size : 48,6 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9781470470340

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Algebraic and Topological Aspects of Representation Theory by Mee Seong Im,Bach Nguyen,Arik Wilbert Pdf

This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20–21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.

Author : K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang
Publisher : American Mathematical Society
Page : 288 pages
File Size : 40,8 Mb
Release : 2024-05-30
Category : Mathematics
ISBN : 9781470472399

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Recent Advances in Noncommutative Algebra and Geometry by K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang Pdf

This volume contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held from June 20–24, 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday. The articles reflect the wide interests of Smith and provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Hopf algebras and quantum groups, the elliptic algebras of Feigin and Odesskii, Calabi-Yau algebras, Artin-Schelter regular algebras, deformation theory, and Lie theory. In addition to original research contributions the volume includes an introductory essay reviewing Smith's research contributions in these fields, and several survey articles.

Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Publisher : American Mathematical Society
Page : 236 pages
File Size : 43,9 Mb
Release : 2023-08-23
Category : Mathematics
ISBN : 9781470473556

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The Diverse World of PDEs by I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky Pdf

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.

Author : Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Publisher : American Mathematical Society
Page : 270 pages
File Size : 48,6 Mb
Release : 2024-04-18
Category : Mathematics
ISBN : 9781470472160

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Recent Developments in Fractal Geometry and Dynamical Systems by Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma Pdf

This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.

Author : Marat V. Markin,Igor V. Nikolaev,Carsten Trunk
Publisher : American Mathematical Society
Page : 250 pages
File Size : 52,9 Mb
Release : 2024-04-09
Category : Mathematics
ISBN : 9781470473051

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Advances in Functional Analysis and Operator Theory by Marat V. Markin,Igor V. Nikolaev,Carsten Trunk Pdf

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.

Author : A. Leroy,S. K. Jain
Publisher : American Mathematical Society
Page : 270 pages
File Size : 51,8 Mb
Release : 2023-05-01
Category : Mathematics
ISBN : 9781470468590

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Algebra and Coding Theory by A. Leroy,S. K. Jain Pdf

This volume contains the proceedings of the Virtual Conference on Noncommutative Rings and their Applications VII, in honor of Tariq Rizvi, held from July 5–7, 2021, and the Virtual Conference on Quadratic Forms, Rings and Codes, held on July 8, 2021, both of which were hosted by the Université d'Artois, Lens, France. The articles cover topics in commutative and noncommutative algebra and applications to coding theory. In some papers, applications of Frobenius rings, the skew group rings, and iterated Ore extensions to coding theory are discussed. Other papers discuss classical topics, such as Utumi rings, Baer rings, nil and nilpotent algebras, and Brauer groups. Still other articles are devoted to various aspects of the elementwise study for rings and modules. Lastly, this volume includes papers dealing with questions in homological algebra and lattice theory. The articles in this volume show the vivacity of the research of noncommutative rings and its influence on other subjects.

Author : Hemen Dutta
Publisher : American Mathematical Society
Page : 256 pages
File Size : 52,5 Mb
Release : 2023-06-12
Category : Mathematics
ISBN : 9781470469641

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Mathematical Modelling by Hemen Dutta Pdf

This volume is a collection of chapters that present several key principles and theories, as well as their potential uses in the development of mathematical models in areas like waves, thermodynamic, electromagnetics, fluid dynamics, and catastrophes. The techniques and methodologies used in this book, on the other hand, should have a long-term impact and be applicable to a wide range of different topics of study and research. Each chapter should also help readers in gaining a better knowledge of the underlying and connected concepts. The companion volume (Contemporary Mathematics, Volume 787) is devoted to theory and application.

Author : Michael A. Jones,David McCune,Jennifer M. Wilson
Publisher : American Mathematical Society
Page : 210 pages
File Size : 53,7 Mb
Release : 2024-03-25
Category : Mathematics
ISBN : 9781470469788

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Mathematical Analyses of Decisions, Voting and Games by Michael A. Jones,David McCune,Jennifer M. Wilson Pdf

This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

Author : Jean-Pierre Magnot
Publisher : American Mathematical Society
Page : 272 pages
File Size : 42,5 Mb
Release : 2024-02-02
Category : Mathematics
ISBN : 9781470472542

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Recent Advances in Diffeologies and Their Applications by Jean-Pierre Magnot Pdf

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.

Author : Peter Crooks,Alexandru I. Suciu
Publisher : American Mathematical Society
Page : 168 pages
File Size : 53,9 Mb
Release : 2023-09-25
Category : Mathematics
ISBN : 9781470469924

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Compactifications, Configurations, and Cohomology by Peter Crooks,Alexandru I. Suciu Pdf

This volume contains the proceedings of the Conference on Compactifications, Configurations, and Cohomology, held from October 22–24, 2021, at Northeastern University, Boston, MA. Some of the most active and fruitful mathematical research occurs at the interface of algebraic geometry, representation theory, and topology. Noteworthy examples include the study of compactifications in three specific settings—algebraic group actions, configuration spaces, and hyperplane arrangements. These three types of compactifications enjoy common structural features, including relations to root systems, combinatorial descriptions of cohomology rings, the appearance of iterated blow-ups, the geometry of normal crossing divisors, and connections to mirror symmetry in physics. On the other hand, these compactifications are often studied independently of one another. The articles focus on new and existing connections between the aforementioned three types of compactifications, thereby setting the stage for further research. It draws on the discipline-specific expertise of all contributors, and at the same time gives a unified, self-contained reference for compactifications and related constructions in different contexts.

Author : A.L. Onishchik
Publisher : Boom Koninklijke Uitgevers
Page : 238 pages
File Size : 55,5 Mb
Release : 2000-02-03
Category : Mathematics
ISBN : 3540505857

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Lie Groups and Lie Algebras II by A.L. Onishchik Pdf

A systematic survey of all the basic results on the theory of discrete subgroups of Lie groups, presented in a convenient form for users. The book makes the theory accessible to a wide audience, and will be a standard reference for many years to come.