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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

Duration30 hours.   First lectureThursday, November 6th.

WhenMondays and Thursdays, 11 AM to 1 PM.

WhereAula "Seminario 1" (with the exception of the lectures on November 6th and 10th, which will be held in "Seminario 2").

TeachersGiuseppe Bargagnati and Francesco Milizia

This course is mainly aimed at PhD students, but Master students are welcome to attend.

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:

• Basic group theory (homomorphisms, actions on sets...);
• Very few fundamentals in topology like fundamental groups and covering maps.

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.