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Author : Emmanuel Breuillard,Hee Oh
Publisher : Cambridge University Press
Page : 375 pages
File Size : 49,5 Mb
Release : 2014-02-17
Category : Mathematics
ISBN : 9781107036857
This collection of survey articles focuses on recent developments at the boundary between geometry, dynamical systems, number theory and combinatorics.
Author : C. M. Campbell,M. R. Quick,E. F. Robertson,C. M. Roney-Dougal
Publisher : Cambridge University Press
Page : 503 pages
File Size : 49,7 Mb
Release : 2015-10-22
Category : Mathematics
ISBN : 9781107514546
Leading researchers survey the latest developments in group theory and many related areas.
Author : Artur Avila,Michael Th. Rassias,Yakov Sinai
Publisher : Springer Nature
Page : 388 pages
File Size : 46,6 Mb
Release : 2022-11-01
Category : Mathematics
ISBN : 9783031053313
Analysis at Large is dedicated to Jean Bourgain whose research has deeply influenced the mathematics discipline, particularly in analysis and its interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain’s discretized sum-product theorem, his work in nonlinear dispersive equations, the slicing problem by Bourgain, harmonious sets, the joint spectral radius, equidistribution of affine random walks, Cartan covers and doubling Bernstein type inequalities, a weighted Prékopa-Leindler inequality and sumsets with quasicubes, the fractal uncertainty principle for the Walsh-Fourier transform, the continuous formulation of shallow neural networks as Wasserstein-type gradient flows, logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators, polynomial equations in subgroups, trace sets of restricted continued fraction semigroups, exponential sums, twisted multiplicativity and moments, the ternary Goldbach problem, as well as the multiplicative group generated by two primes in Z/QZ. It is hoped that this volume will inspire further research in the areas of analysis treated in this book and also provide direction and guidance for upcoming developments in this essential subject of mathematics.
Author : Mladen Bestvina,Michah Sageev,Karen Vogtmann
Publisher : American Mathematical Soc.
Page : 339 pages
File Size : 53,6 Mb
Release : 2014-12-24
Category : Mathematics
ISBN : 9781470412272
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Author : Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil
Publisher : Walter de Gruyter GmbH & Co KG
Page : 386 pages
File Size : 49,7 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110667028
This book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.
Author : Bjorn Poonen
Publisher : American Mathematical Soc.
Page : 337 pages
File Size : 42,7 Mb
Release : 2017-12-13
Category : Algebraic varieties
ISBN : 9781470437732
This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
Author : Jayce R. Getz
Publisher : Springer Nature
Page : 611 pages
File Size : 52,8 Mb
Release : 2024-06-13
Category : Electronic
ISBN : 9783031411533
Author : John Voight
Publisher : Springer Nature
Page : 877 pages
File Size : 53,8 Mb
Release : 2021-06-28
Category : Mathematics
ISBN : 9783030566944
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Author : C. M. Campbell,C. W. Parker,M. R. Quick,E. F. Robertson,C. M. Roney-Dougal
Publisher : Cambridge University Press
Page : 510 pages
File Size : 45,7 Mb
Release : 2019-04-11
Category : Mathematics
ISBN : 9781108728744
These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.
Author : James W. Cogdell,Günter Harder,Stephen Kudla,Freydoon Shahidi
Publisher : Springer
Page : 304 pages
File Size : 40,9 Mb
Release : 2018-08-18
Category : Mathematics
ISBN : 9783319955490
This book discusses the mathematical interests of Joachim Schwermer, who throughout his career has focused on the cohomology of arithmetic groups, automorphic forms and the geometry of arithmetic manifolds. To mark his 66th birthday, the editors brought together mathematical experts to offer an overview of the current state of research in these and related areas. The result is this book, with contributions ranging from topology to arithmetic. It probes the relation between cohomology of arithmetic groups and automorphic forms and their L-functions, and spans the range from classical Bianchi groups to the theory of Shimura varieties. It is a valuable reference for both experts in the fields and for graduate students and postdocs wanting to discover where the current frontiers lie.
Author : Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Publisher : Cambridge University Press
Page : 341 pages
File Size : 53,6 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781107552371
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Author : Richard J. Nowakowski
Publisher : Cambridge University Press
Page : 351 pages
File Size : 44,7 Mb
Release : 2015-04-16
Category : Mathematics
ISBN : 9781107011038
A mathematical explanation of misere games, in which losing is the goal.
Author : Emmanuel Kowalski
Publisher : Cambridge University Press
Page : 271 pages
File Size : 54,5 Mb
Release : 2021-05-06
Category : Mathematics
ISBN : 9781108840965
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.
Author : David Fisher,Dmitry Kleinbock,Gregory Soifer
Publisher : University of Chicago Press
Page : 573 pages
File Size : 55,7 Mb
Release : 2022-02-07
Category : Mathematics
ISBN : 9780226804163
This definitive synthesis of mathematician Gregory Margulis’s research brings together leading experts to cover the breadth and diversity of disciplines Margulis’s work touches upon. This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. Dynamics, Geometry, Number Theory introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sections—“Arithmeticity, Superrigidity, Normal Subgroups”; “Discrete Subgroups”; “Expanders, Representations, Spectral Theory”; and “Homogeneous Dynamics”—the chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge.
Author : Alla Detinko,Michael Kapovich,Alex Kontorovich,Peter Sarnak,Richard Schwartz
Publisher : American Mathematical Society
Page : 164 pages
File Size : 48,6 Mb
Release : 2023-03-10
Category : Mathematics
ISBN : 9781470468040
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.