Tuesday, April 25, 2023
Time  Items 

All day 

4:00pm 
04/25/2023  4:15pm The classification of finite subgroups of SO(3) is a classical problem in geometry. In this talk, we will welcome in the much larger class of rational rotation groups and see what sense can be made of such groups. Call a subgroup G of SO(3,Q) primary if it is discrete in some padic topology. These groups are essentially free groups, and we’ll consider them wellunderstood. We entertain the possibility that any subgroup of SO(3,Q) which is not abelian or primary might be forced to be arithmetic, meaning that it looks a lot like SO(3,A) for a subring A of Q. We prove some results supporting this conjecture, including some special cases of the conjecture and a rigidity result. This conjecture has many analogues in the broader study of discrete subgroups of Lie groups, and has many consequences in geometry and group theory. Location:
LOM 206
