Rice University

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Colloquium

Mathematics

Speaker: Misha Kapovich
UC Davis

Colloquium: Polyhedral complexes and topology of projective varieties

Thursday, April 5, 2012
4:00 PM  to 5:00 PM

227  Herman Brown Hall
Rice University
6100 Main St
Houston, Texas, USA

Polyhedral complexes are obtained by gluing convex polytopes (say, Euclidean or hyperbolic) via isometric maps. In the talk I will explain how to use such complexes to construct irreducible complex-projective varieties with controlled singularities (normal crossings and Whitney umbrellas) and with prescribed fundamental groups. Polyhedral complexes that appear in the construction come from geometric topology of 1960s and 3-dimensional hyperbolic geometry (Dirichlet fundamental domains of some discrete isometry groups of hyperbolic 3-space). This is partly a joint work with Janos Kollar.

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