## Departmental Colloquium

Jeff Brock

Brown University

Entomology and morphology in hyperbolic geometry

**Abstract:**The classification of hyperbolic 3-manifolds with finitely generated fundamental group involves sorting a lot of pretty ugly looking bugs. Geometrically, this classification reduces to Thurston's

*Ending Lamination Conjecture*; our proof (with Canary and Minsky) produced an array of tools for understanding how a topological specification of a 3-manifold relates to its "shape" or geometry. One such specification, the

*Heegaard splitting*, seems ripe for exploration along these lines, yet a complete picture is still under development. I'll review the state of things, and discuss some key examples.

Friday April 11, 2014 at 3:00 PM in SEO 636