Thursday, February 8
Time: 4:00 p.m.
Location: 114 McAllister Building
Name: Richard Schwartz
Affiliation: Brown University
Title: Triangle groups, complex hyperbolic geometry, and Dehn surgery
Abstract: The triangle groups are especially pretty symmetry groups of the hyperbolic plane. In the first part of my talk I will explain these groups. In the second part of my talk I will introduce the complex hyperbolic plane, a space that relates to the ordinary hyperbolic plane much in the way that C2 relates to R2, and show how the triangle groups act on the complex hyperbolic plane in many ways. Most things about these actions are unknown and I'll explain some of the open problems. In the third part of my talk I'll sketch some of my results related to these groups. The highlights are a complex hyperbolic version of Thurston's Dehn surgery theorem, the resolution of the "generalized Goldman-Parker conjecture" in some cases, and the construction of the only known hyperbolic 3-manifolds that bound complex hyperbolic manifolds.