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401-3381-74L 4 Credits DR , MSC D-MATH

Growth in Groups

Lecturers & Examiners: Dr. Simon Machado
VVZ CR n/a

Last Updated: 2026-02-05 16:29:40

Abstract

This is an introduction to the study of growth in groups which lies at the interface of group theory, geometry, probability and combinatorics.We will first give an overview of classical results (i.e. Gromov’s polynomial growth theorem) and applications to geometry, dynamics and number theory. But our main goal will be recent advances and, in particular, the ‘product theorem’ in SL_n.

Content

The topics covered in this class will include (but are not limited to): additive combinatorics in non-commutative groups, Gromov’s polynomial growth theorem, doubling and tripling inequalities in groups, the Larsen—Pink inequality, escape of subvarieties, approximate groups, and the product theorem.

Resources

Literature

1) Expansion in finite simple groups of Lie type, Terence Tao, Graduate Studies in Mathematics, vol. 164, AMS, 2015. 2) Introduction to approximate groups, Matthew Tointon, London Mathematical Society Student Texts series, Cambridge University Press, 2020. 3) A brief introduction to approximate groups, Emmanuel Breuillard, MSRI publications, vol. 61, 2013.

General Information

Language
English
Levels
DR , MSC

Examination

Type
session examination
Mode
oral 25 minutes
The exam is only offered in the two examination sessions Winter 2025 and Summer 2025.The effective duration of the exam is 20 minutes.For technical reasons it shows 25min.

Course Components

Type Title Time & Place Hours
lecture Growth in Groups
  • Thu 14:15-16:00 (HG D 5.2)
2 h weekly

Offered In