This is the website for the reading group on Approximate Groups that we are holding in the Spring semester 2024/25 in Ljubljana.
The main reference is the book Introduction to Approximate Groups by Matthew Tointon.
Each participant chooses a topic and prepares a one hour lecture for the group. You do not need to cover the entire material in great detail and it is perfectly fine to focus on explaining the main ideas.
If you decide to participate, please send an email to urban.jezernik@fmf.uni-lj.si so I can mark the topic as chosen.
A list of topics, along with references, is available here (prepared by Matevž Miščič).
Basic Concepts (Marco Barbieri)
Some sets of small doubling in Abelian groups (Miloš Puđa)
Convex geometry and lattices (Daniel Smertnig)
Fourier analysis and small doubling in Abelian groups (Roman Bessonov)
Nilpotent groups (Jakob Jurij Snoj)
Nilpotent approximate groups, Arbitrary approximate groups and residually nilpotent approximate groups (Borislav Kirilov)
Soluble approximate subgroups of GL_n(C) (Matevž Miščič)
Arbitrary approximate subgroups of GL_n(C) (Matevž Miščič)
Applications -- A refinement of Gromov’s theorem (Miloš Puđa)
Applications -- Diameters of finite groups (Urban Jezernik)
We meet on Mondays at 14-15 in classroom 3.06.
24/02/2025 Matevž Miščič: Introductory meeting [video]
10/03/2025 Marco Barbieri: Basic Concepts [video]
17/03/2025 Miloš Puđa: Some sets of small doubling in Abelian groups [video]
24/03/2025 Daniel Smertnig: Convex geometry and lattices [video]
31/03/2025 Roman Bessonov: Fourier analysis and small doubling in abelian groups [video]
07/04/2025 Jianan Peng: Fourier analysis and small doubling in abelian groups, part 2 [video]
14/04/2025 Jakob Jurij Snoj: Nilpotent groups [video]
05/05/2025 Borislav Kirilov: (Residually) nilpotent approximate groups & Arbitrary approximate groups [video]
12/05/2025 Matevž Miščič: Soluble approximate subgroups of GLn(C) [video]
19/05/2025 Matevž Miščič: Arbitrary approximate subgroups of GLn(C) [video]
26/05/2025 Miloš Puđa: Applications -- A refinement of Gromov's theorem [video]
02/06/2025 Urban Jezernik: Applications -- Diameters of finite groups