Introduction to Approximate Groups

Description

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 The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples.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.

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 Universite de Paris-Sud and at the Universite de Neuchatel, 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.

'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