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Description

Knot Floer homology is a refinement of Heegaard Floer homology, providing an invariant for a pair (a 3-manifold, a knot in it). Recently, in collaboration with P. Ozsvath and Z. Szabo, we have found a 1-parameter 'deformation' of knot Floer homology for knots in S^3, leading to a family of concordance invariants. For the value t=1 the deformation admits a further symmetry, providing a bound on the unoriented 4 ball genus (smooth crosscap number) of the knot at hand. In the lecture I plan to recall the basic constructions behind knot Floer homology, list its basic properties, and show how the deformation works. Using grid diagrams we will discuss a sketch of the proof of the genus bounds.