Some Results in Complex Hyperbolic Geometry

Some Results in Complex Hyperbolic Geometry

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Luca Di Cerbo, Duke University
Fine Hall 401

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.