Complexity And Randomness In Group Theory
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Complexity and Randomness in Group Theory
Author | : Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 412 |
Release | : 2020-06-08 |
Genre | : Mathematics |
ISBN | : 9783110667523 |
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Detailed Description
Complexity and Randomness in Group Theory
Author | : Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 386 |
Release | : 2020-06-08 |
Genre | : Mathematics |
ISBN | : 9783110667028 |
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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.
Non commutative Cryptography and Complexity of Group theoretic Problems
Author | : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov |
Publsiher | : American Mathematical Soc. |
Total Pages | : 402 |
Release | : 2011 |
Genre | : Computers |
ISBN | : 9780821853603 |
Download Non commutative Cryptography and Complexity of Group theoretic Problems Book in PDF, Epub and Kindle
Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.
Topological and Asymptotic Aspects of Group Theory
Author | : R. I. Grigorchuk |
Publsiher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 9780821837566 |
Download Topological and Asymptotic Aspects of Group Theory Book in PDF, Epub and Kindle
The articles in this volume are based on the talks given at two special sessions at the AMS Sectional meetings held in 2004. The articles cover various topological and asymptotic aspects of group theory, such as hyperbolic and relatively hyperbolic groups, asymptotic cones, Thompson's group, Nielsen fixed point theory, homology, groups acting on trees, groups generated by finite automata, iterated monodromy groups, random walks on finitely generated groups, heat kernels, and currents on free groups.
Groups and Model Theory
Author | : Olga Kharlampovich,Rizos Sklinos |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 250 |
Release | : 2021-05-10 |
Genre | : Mathematics |
ISBN | : 9783110719765 |
Download Groups and Model Theory Book in PDF, Epub and Kindle
This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .
Elementary Theory of Groups and Group Rings and Related Topics
Author | : Paul Baginski,Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Vladimir Shpilrain |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 272 |
Release | : 2020-02-10 |
Genre | : Mathematics |
ISBN | : 9783110638387 |
Download Elementary Theory of Groups and Group Rings and Related Topics Book in PDF, Epub and Kindle
This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.
Computational and Statistical Group Theory
Author | : Robert H. Gilman,Nev.) AMS Special Session Geometric Group Theory (2001 : Las Vegas,Alexei G. Myasnikov,Vladimir Shpilrain |
Publsiher | : American Mathematical Soc. |
Total Pages | : 138 |
Release | : 2002 |
Genre | : Combinatorial group theory |
ISBN | : 9780821831588 |
Download Computational and Statistical Group Theory Book in PDF, Epub and Kindle
This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ). It is suitable for graduate students and research mathematicians interested in group theory.
Kolmogorov Complexity and Algorithmic Randomness
Author | : A. Shen,V. A. Uspensky,N. Vereshchagin |
Publsiher | : American Mathematical Society |
Total Pages | : 511 |
Release | : 2022-05-18 |
Genre | : Mathematics |
ISBN | : 9781470470647 |
Download Kolmogorov Complexity and Algorithmic Randomness Book in PDF, Epub and Kindle
Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.