Date:
Thu, 08/05/202510:00-11:00
Location:
Ross 70
Groups and dynamics seminar
Time: Thursday, May 8, 10:00
Place: Ross 70
Speaker: Amir Weiss Behar (HUJI)
Title: Profinite non-rigidity of arithmetic groups
Abstract:
A group is called profinitely rigid if it can be recognized only by looking at its finite quotients. It is still unknown whether SL(n,Z) is profinitely rigid. While not addressing this question, I will construct finite index subgroups of it which are not profinitely rigid (when n ≥ 3). These constructions can be generalized to show that a "typical" arithmetic group exhibits non-isomorphic finite index subgroups whose profinite completions are isomorphic. If time permits I will explain why this can not happen in the exceptional cases.
Time: Thursday, May 8, 10:00
Place: Ross 70
Speaker: Amir Weiss Behar (HUJI)
Title: Profinite non-rigidity of arithmetic groups
Abstract:
A group is called profinitely rigid if it can be recognized only by looking at its finite quotients. It is still unknown whether SL(n,Z) is profinitely rigid. While not addressing this question, I will construct finite index subgroups of it which are not profinitely rigid (when n ≥ 3). These constructions can be generalized to show that a "typical" arithmetic group exhibits non-isomorphic finite index subgroups whose profinite completions are isomorphic. If time permits I will explain why this can not happen in the exceptional cases.