Eaman Eftekhary
Heegaard Floer theory and invariants of 3-manifolds and knots inside them.

 We review some of the main developments in Heegaard Floer theory in the past 15 years. In particular, this includes the applications to the study of 3-manifolds, as well as the construction of knot and link invariants. Our focus will be on a number of classical problems, namely, using Heegaard Floer theory to distinguish the  standard sphere from other 3-manifolds, detection of the Seifert genus of a knot and lower bounds on the unknotting number. Part of the work reported in this talk is joint work with A. Alishahi.