Some Results in Complex Hyperbolic Geometry

Thursday, October 24, 2013 -
4:30pm to 5:30pm
PLEASE NOTE SPECIAL DAY AND LOCATION.  In this talk, I present a new approach to the study of cusped complex hyperbolic manifolds through their compactifications. Among other things, I give effective bounds on the number of complex hyperbolic manifolds with given upper bound on the volume. Moreover, I estimate the number of cuspidal ends of such manifolds in terms of their volume. Finally, I address the classification problem for cusped complex hyperbolic surfaces with minimal volume. This is the noncompact or logarithmic analogue of the well known classification problem for fake projective planes.
Speaker: 
Luca Di Cerbo
Duke University
Event Location: 
Fine Hall 401