Cusps of arithmetic orbifolds

Geometry & Topology
Event time: 
Tuesday, January 12, 2010 - 11:30am to Monday, January 11, 2010 - 7:00pm
Matthew Stover
Speaker affiliation: 
University of Texas at Austin
Event description: 

I will describe how to determine the number of cusps for maximal arithmetic subgroups of certain semisimple Lie groups, focusing on SU(2, 1), which builds upon earlier work of Zink and generalizes work of Helling and Chinburg-Long-Reid, who considered SL(2,R) and SL(2,C), respectively. Consequentially, for all N, an arithmetic complex hyperbolic 2-orbifold with N cusps lies in one of finitely many commensurability classes. (For N = 1 there are at least 26.) Given time, I will explain how this philosophy generalizes to other semisimple groups.