4:00 pm Thursday, August 25, 2011

Ciprian Manolescu (UCLA - Math)

Starting with the work of Donaldson in the 1980s, gauge theory has been used to get nontrivial information about smooth 4-manifolds. Heegaard Floer theory is a symplectic replacement for gauge theory, with similar topological applications. Recently, the Heegaard Floer invariants (of knots, links, 3-manifolds, and 4-manifolds) were shown to be algorithmically computable. In particular, this gives a simple algorithm for detecting the genus of a knot.