Akram Alishahi, Peter Lambert-Cole and Gordana Matic. Heegaard Floer theory is a package of powerful algebraic invariants for low dimensional objects such as 3- and 4-manifolds, knots and links, contact structures, etc. These invariants have answered several long-standing open questions in low dimensional topology, in particular in dimension 3, and have been very effective for studying contact and symplectic structures as well. Our groups works on developing new Heegaard Floer theoretic invariants for studying low dimensional phenomena including contact structures, unknotting number, knot and link concordance groups, and surface diffeomorphisms, studies their topological applications and investigate their connections and similarities with Khovanov-type theories.
