Events Calendar
WDSS Intermediate R Workshop
April 22, 2024

PhD Public Lecture (Math) - Michal Cizek

Date:
Friday, June 17, 2022
Time:
9:30 am
Location:
Virtual via Zoom
Cost:
Free

Automorphism-preserving color substitutions on Profinite Graphs


Profinite groups are topological groups which are known to be Galois groups. Their free product was extensively studied by Luis Ribes and Pavel Zaleskii using the notion of a profinite graph and having profinite groups act freely on such graphs.

We will use a different approach to study profinite groups using profinite graphs and that is with the notion of automorphisms and colors. We will generalize to profinite graphs: the theorem of Frucht (1939) that shows that every finite group is a group of automorphisms of a finite connected graph, and we will give a profinite analog of the theorem of Sabidussi (1959)  that states that every abstract group is a group of automorphisms of a connected graph.

Our version of those theorems will be: Every finitely generated profinite group is a group of continuous automorphisms of a profinite graph with a closed set of edges and every profinite group is a group of continuous automorphisms of a connected profinite graph.

Finally, we will give an application of these theorems, which is a partial solution to the conjecture of Sidney Morris and Karl Hoffmann stating that every profinite group is a group of autohomeomorphisms of a connected compact Hausdorff space. We will show this to be true for finitely generated profinite groups.

Contact:
Adriana Dimova
adimova2@uwo.ca


Powered by Blackbaud
nonprofit software