Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics
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Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics
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Author : Aaron Wootton
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-03
Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics written by Aaron Wootton and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.
Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.
Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics
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Author : Aaron Wootton
language : en
Publisher:
Release Date : 2022
Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics written by Aaron Wootton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Automorphisms categories.
Problems On Mapping Class Groups And Related Topics
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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-09-12
Problems On Mapping Class Groups And Related Topics written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Mathematics categories.
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Research Connections
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Author : Abra Brisbin
language : en
Publisher: Springer Nature
Release Date : 2025-02-18
Research Connections written by Abra Brisbin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-18 with Mathematics categories.
What does math research really look like? Which subfield is right for me? Do people like me go to graduate school, and succeed? This book provides students a “sneak preview” of math research in a variety of subfields. Each chapter features the work of a different mathematician along with enough background material for an advanced undergraduate or early graduate student to understand the key ideas and get a sense for the styles of thinking involved in each subfield. Each chapter is prefaced by a short biography of the mathematician who wrote the chapter (all people connected to the Carleton College Summer Math Program for Women), providing advice and examples of paths from undergraduate education, through graduate school and beyond. This book provides a source of ideas and starting points for in-class projects, independent studies, and student talks as well as supplementary reading in courses. The profiles of early career mathematicians and statisticians at the beginning of each chapter are valuable as an advising resource for students considering graduate school, or to show students a diverse view of modern mathematicians in a “Math for Liberal Arts”-style course.
Computational Aspects Of Discrete Subgroups Of Lie Groups
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Author : Alla Detinko
language : en
Publisher: American Mathematical Society
Release Date : 2023-03-10
Computational Aspects Of Discrete Subgroups Of Lie Groups written by Alla Detinko and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-10 with Mathematics categories.
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.
Geometric And Functional Inequalities And Recent Topics In Nonlinear Pdes
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Author : Emanuel Indrei
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-09
Geometric And Functional Inequalities And Recent Topics In Nonlinear Pdes written by Emanuel Indrei and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-09 with Mathematics categories.
This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.
Algebraic And Topological Aspects Of Representation Theory
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Author : Mee Seong Im
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-22
Algebraic And Topological Aspects Of Representation Theory written by Mee Seong Im and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-22 with Mathematics categories.
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.
Recent Advances In Diffeologies And Their Applications
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Author : Jean-Pierre Magnot
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-02
Recent Advances In Diffeologies And Their Applications written by Jean-Pierre Magnot and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-02 with Mathematics categories.
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.
Mathematical Modelling
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Author : Hemen Dutta
language : en
Publisher: American Mathematical Society
Release Date : 2023-06-12
Mathematical Modelling written by Hemen Dutta and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-12 with Mathematics categories.
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.
The Diverse World Of Pdes
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Author : I. S. Krasil′shchik
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-21
The Diverse World Of Pdes written by I. S. Krasil′shchik and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-21 with Mathematics categories.
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 the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.