2019 - Geometric Group Theory

Overview. Geometric Group Theory studies relations between algebraic properties of groups and geometric properties of the spaces on which they act on. It often borrows language from and has interactions with other parts of Mathematics such as geometry, analysis, topology, computer science and cryptography.

IMPORTANT: this course bears the same name as a Master’s (Laurea Magistrale) course by Thomas Weigel, but the syllabus is very different (see below). This is NOT the same course.

When. Every Tuesday @ 10am - 12pm and @ 2pm - 4pm from October 21st to December 3rd

Laurea magistrale’s students are encouraged to participate too, even if they cannot earn credits (CFU) from this course.

Enrolled students will likely give a seminar at the end of the course from a selection of topics.

Where. The department of Mathematics and Applications (building U5) of the Università degli Studi di Milano - Bicocca.

Contacts. francesco.matucci@unimib.it

Abstract. The plan of the course is to learn about:

(1) Cayley graphs and quasi-isometries

(2) Dehn functions and hyperbolic groups

(3) Paradoxical decompositions and amenable groups

(4) Growth and self-similar groups

References. We will mostly follow some course notes. Other relevant textbooks are

C. Löh, Geometric group theory, an introduction, Springer Universitext, 2017

M. Clay and D. Margalit, Office hours with a geometric group theorist, Princeton University Press, 2017

M. Bridson, A. Haefliger, Metric spaces of non-positive curvature, Springer, 1999

P. de la Harpe, Topics on Geometric Group Theory, Chicago Lectures in Mathematics, University of Chicago Press, 2000

S. Wagon, The Banach-Tarski paradox, Cambridge University Press, 1985