Cartesian Products as Profinite Completions and Representation Growth of Groups

LIE GROUPS, REPRESENTATIONS AND DISCRETE MATH
Topic:Cartesian Products as Profinite Completions and Representation Growth of Groups
Speaker:Martin Kassabov
Affiliation:Cornell University
Date:Tuesday, March 21
Time/Room:4:00pm - 5:00pm/S-101

We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely Generated residually finite group. The same holds for Cartesian products of other simple groups under some natural restrictions. Using this construction we can show that there exist finitely generated groups with (almost) arbitrary representation growth. (joint work with N. Nikolov)