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