Seminar:
Hahn Lecture Series
Event time:
Thursday, April 3, 2025 - 4:00pm
Location:
KT207
Speaker:
Emmanuel Breuillard
Speaker affiliation:
University of Oxford
Event description:
In this third lecture, I will talk about random groups and their linear representations. Introduced by Gromov in the 80s, random groups provide a wealth of examples of finitely presented groups. With O. Becker and P. Varju, we have undertaken the study of their character variety, that is the moduli space of their representations with values in SL(2,C) or a more general semisimple algebraic group. I will show how new families of Zariski-dense rigid groups arise this way and what it tells us about the geometry of word maps. The method showcases a delicate interplay between characteristic zero and characteristic p and relies on GRH.