Introduction to Approximate Groups

Matthew C. H. Tointon (University of Cambridge)

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English

Cambridge University Press
14 November 2019

Discrete mathematics; Groups & group theory; Combinatorics & graph theory

Series: London Mathematical Society Student Texts

Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.

By: Matthew C. H. Tointon (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 156mm, Spine: 17mm
Weight: 430g
ISBN: 9781108470735
ISBN 10: 1108470734
Series: London Mathematical Society Student Texts
Pages: 216
Publication Date: 14 November 2019
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Introduction; 2. Basic concepts; 3. Coset progressions and Bohr sets; 4. Small doubling in abelian groups; 5. Nilpotent groups, commutators and nilprogressions; 6. Nilpotent approximate groups; 7. Arbitrary approximate groups; 8. Residually nilpotent approximate groups; 9. Soluble approximate subgroups GLn(C); 10. Arbitrary approximate subgroups of GLn(C); 11. Applications to growth in groups; References; Index.

Matthew C. H. Tointon is the Stokes Research Fellow at Pembroke College, Cambridge, affiliated to the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He has held postdoctoral positions at Homerton College, Cambridge, at the Université de Paris-Sud and at the Université de Neuchâtel, Switzerland. Tointon is the author of numerous research papers on approximate groups and he proved the strongest known results describing the structure of nilpotent and residually nilpotent approximate groups.

Reviews for Introduction to Approximate Groups

'The book now under reviews offers an excellent introduction … the book is very nicely written, Researchers and fledgling researchers in this area will want to own this book.' Mark Hunacek, The Mathematical Gazette