## Topology Seminar (Main Talk): Commensurators of thin subgroups of $PSL_2(Z)$

Seminar | February 13 | 4-5 p.m. | 3 Evans Hall

Thomas Koberda, University of Virginia

Department of Mathematics

A celebrated result of Margulis says that among irreducible lattices in higher rank semi-simple Lie groups, arithmetic lattices are characterized as those having dense commensurators. If the subgroup of the Lie group is Zariski dense and discrete but is no longer assumed to have finite covolume (that is, to be thin), then no such definitive dichotomy exists. A heuristic due to Y. Shalom says that thin subgroups should be thought of as non-arithmetic. In this talk I will discuss a theorem confirming Shalom's heuristic for certain naturally defined thin subgroups of $PSL_2(Z)$. This is joint work with M. Mj.

c_abbott@berkeley.edu