Date: 11 October 2019
Location: Hempfield High School, Room 213
 Speaker: Matthew Stover, Temple University
   Title: Geometric consequences of (non)arithmeticity

Abstract: In his influential Bulletin of the AMS article,
W. Thurston posed 24 problems that have shaped low-dimensional topology
since. Among them was: "Find topological and geometric properties of
quotient spaces of arithmetic subgroups of PSL(2,C). These manifolds
often seem to have special beauty." The purpose of my talk will be to
motivate this question through totally geodesic surfaces in hyperbolic
3-manifolds. In particular, I will discuss the following geometric
characterization of arithmeticity, which is joint work with Uri Bader,
David Fisher, and Nicholas Miller: If M is a hyperbolic 3-manifold
containing a properly immersed totally geodesic surface, then M is
arithmetic if and only if it contains infinitely many such
surfaces. This answered a question asked independently by Alan Reid and
Curtis McMullen. I will not assume any background except elementary
geometry and topology.