Measure Category And The Cofinality Of The Infinite Symmetric Group
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Dynamical Numbers: Interplay between Dynamical Systems and Number Theory
Author | : S. F. Koli︠a︡da |
Publisher | : American Mathematical Soc. |
Total Pages | : 258 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821849581 |
This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.
A Concise Course in Algebraic Topology
Author | : J. P. May |
Publisher | : University of Chicago Press |
Total Pages | : 262 |
Release | : 1999-09 |
Genre | : Mathematics |
ISBN | : 9780226511832 |
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Model Categories
Author | : Mark Hovey |
Publisher | : American Mathematical Soc. |
Total Pages | : 229 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821843613 |
Model categories are used as a tool for inverting certain maps in a category in a controllable manner. They are useful in diverse areas of mathematics. This book offers a comprehensive study of the relationship between a model category and its homotopy category. It develops the theory of model categories, giving a development of the main examples.
Infinite Dimensional Harmonic Analysis Iii - Proceedings Of The Third German-japanese Symposium
Author | : Kimiaki Saito |
Publisher | : World Scientific |
Total Pages | : 366 |
Release | : 2005-11-09 |
Genre | : Mathematics |
ISBN | : 9814478997 |
This volume contains contributions on recent results in infinite dimensional harmonic analysis and its applications to probability theory. Some papers deal with purely analytic topics such as Frobenius reciprocity, diffeomorphism groups, equivariant fibrations and Harish-Chandra modules. Several other papers touch upon stochastic processes, in particular Lévy processes. The majority of the contributions emphasize on the algebraic-topological aspects of the theory by choosing configuration spaces, locally compact groups and hypergroups as their basic structures. The volume provides a useful survey of innovative work pertaining to a highly actual section of modern analysis in its pure and applied shapings.
The Philosopher's Index
Author | : |
Publisher | : |
Total Pages | : 736 |
Release | : 1990 |
Genre | : Philosophy |
ISBN | : |
Vols. for 1969- include a section of abstracts.
Weil's Conjecture for Function Fields
Author | : Dennis Gaitsgory |
Publisher | : Princeton University Press |
Total Pages | : 320 |
Release | : 2019-02-19 |
Genre | : Mathematics |
ISBN | : 0691184437 |
A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil’s conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting l-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors. Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil’s conjecture. The proof of the product formula will appear in a sequel volume.
Notes on Infinite Permutation Groups
Author | : Meenaxi Bhattacharjee |
Publisher | : Springer |
Total Pages | : 206 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540498133 |
The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.