Title: Trivial tangles and Floer homology

Abstract: Tangles are pieces of knots. After introducing tangles, two notions of equivalence for them, and some examples and (knot-theoretic) uses of them, we will sketch an invariant which can be used to check if tangles are boundary parallel—one notion of triviality for tangles. This is joint work with A. Alishahi, building on earlier work with P. Ozsvath and D. Thurston.