Profinite Graphs and Groups
Profinite Graphs and Groups

Author: Luis Ribes

Publisher: Springer

Published: 2017-08-23

Total Pages: 473

ISBN-13: 3319611992

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This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open questions and suggestions for further reading.

Field Arithmetic
Field Arithmetic

Author: Michael D. Fried

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 475

ISBN-13: 3662072165

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Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?

What's Next?
What's Next?

Author: Dylan Thurston

Publisher: Princeton University Press

Published: 2020-07-07

Total Pages: 436

ISBN-13: 069116777X

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William Thurston (1946-2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of mathematical fields, from foliations, contact structures, and Teichm ller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. What's Next? brings together many of today's leading mathematicians to describe recent advances and future directions inspired by Thurston's transformative ideas. Including valuable insights from his colleagues and former students, What's Next? discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. This incisive and wide-ranging book also explores how he introduced new ways of thinking about and doing mathematics, innovations that have had a profound and lasting impact on the mathematical community as a whole.

Ischia Group Theory 2008 - Proceedings Of The Conference In Group Theory
Ischia Group Theory 2008 - Proceedings Of The Conference In Group Theory

Author: Mariagrazia Bianchi

Publisher: World Scientific

Published: 2009-07-30

Total Pages: 315

ISBN-13: 981446743X

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The volume contains a collection of research articles by leading experts in group theory, and reports of several accessible surveys of recent research in the area. The compilation provide an overview of the diversity of themes and applications that interest today's group theorists. The topics covered in this volume include: character theory, combinatorial group theory, varieties of groups, conjugacy classes, profinite groups, graphs connected with groups, subgroup structure, representation theory.

Analysis and Geometry on Graphs and Manifolds
Analysis and Geometry on Graphs and Manifolds

Author: Matthias Keller

Publisher: Cambridge University Press

Published: 2020-08-20

Total Pages: 493

ISBN-13: 1108587380

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This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.

The q-theory of Finite Semigroups
The q-theory of Finite Semigroups

Author: John Rhodes

Publisher: Springer Science & Business Media

Published: 2009-04-05

Total Pages: 674

ISBN-13: 0387097813

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This comprehensive, encyclopedic text in four parts aims to give the reader — from the graduate student to the researcher/practitioner — a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature.

Profinite Groups
Profinite Groups

Author: Luis Ribes

Publisher: Springer Science & Business Media

Published: 2013-04-09

Total Pages: 441

ISBN-13: 3662040972

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This self-contained book serves both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. It contains complete and clear proofs for most results, many of which appear here in book form for the first time. Suitable as a basis for courses.

Developments in Language Theory
Developments in Language Theory

Author: Nelma Moreira

Publisher: Springer Nature

Published: 2021-08-06

Total Pages: 394

ISBN-13: 3030815080

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This book constitutes the proceedings of the 25th International Conference on Developments in Language Theory, DLT 2021, which was held in Porto, Portugal, during August 16-20, 2021. The conference took place in an hybrid format with both in-person and online participation. The 27 full papers included in these proceedings were carefully reviewed and selected from 48 submissions. The DLT conference series provides a forum for presenting current developments in formal languages and automata. Its scope is very general and includes, among others, the following topics and areas: grammars, acceptors and transducers for words, trees and graphs; algebraic theories of automata; algorithmic, combinatorial, and algebraic properties of words and languages; variable length codes; symbolic dynamics; cellular automata; polyominoes and multidimensional patterns; decidability questions; image manipulation and compression; efficient text algorithms; relationships to cryptography, concurrency, complexity theory, and logic; bio-inspired computing; quantum computing. The book also includes 3 invited talks in full paper length.