Francesco Milizia
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Groups acting on trees and related topics in geometric group theory

University of Bologna, Dipartimento di Matematica, Nov 2025 - Jan 2026

TeachersGiuseppe Bargagnati and Francesco Milizia

Duration30 hours.   First lectureThursday, November 6th.

WhenMondays and Thursdays, 11 AM to 1 PM.

WhereAula "Seminario 1" (exception: on December 18 we are in "Seminario 2").

Short description of the course The main topic of the course is the study of groups via their actions on trees (graphs without closed loops). Understanding such actions often gives great insights about the algebraic structure of the acting group. After having presented the general theory, the last part of the course will focus on its applications and on related topics in geometric group theory.

Prerequisites We expect familiarity with:

Later in the course, we will make some use of singular homology of topological spaces, but the "core part" of the course will not use it.

This course is mainly aimed at PhD students, but all interested students are welcome to attend. If you are a student at UniBo, we invite you to enrol at the Virtuale page (you are not required to be a PhD student).

This file contains a set of exercises for reviewing the topics of the course. Moreover, it collects many definitions and pieces of notation used in the course. It gets updated regularly.

(updated: 17 nov)

Here, we collect (unpolished) lecture notes.