Discussion of topics for this semester
Braid groups are well known for being studied in many different areas of Mathe- matics thanks to the variety of approaches one can use to define them.
During the seminar we see most of these approaches, and we learn how they were used through the years to prove relevant properties such as torsion-freeness, hopfi- anity and residual finiteness and furthermore, to answer the word and conjugacy problems.
For our purposes, we follow the notes by Gonzalez-Meneses [1], which cover almost all the basics and collect often multiple proofs of the same results, so to gain a parallel view over all the approaches.
Due to the conciseness of such notes, I suggest to integrate the material -whenever required- with Chapter 1 of Kassel-Turaev’s textbook [2] and/or follow the references already cited in [1].
See the programme for more details.
Main reference:
The idea is to have an introduction to the classical theory of Sigma-invariants for discrete groups, with a particular focus on the first invariant Σ1, mentioning some of the applications in group theory. If time will permit, we will conclude with a talk on the generalisation of Σ1 to locally compact groups.
Research talks
Bass-Serre theory
Totally disconnected locally compact groups
Mixed Topics
Word Growth in Groups
Bass-Serre Theory and Profinite Analogues
p-Adic analytic pro-p groups
Invariant random subgroups
Probabilistic methods in group theory
Buildings