Title: Bridge number and tangle product of knots
Abstract: Tangle product is a very general operation in which two knots are amalgamated together to create a third. The operation of tangle product generalizes both connected sum and Conway product of knots. The bridge number of a knot is the fewest number of maxima necessary to form an embedding of the knot in 3-space. I will present results showing that, under certain hypotheses involving the distance of a minimal bridge surface in the curve complex, the bridge number of a tangle product is at least the sum of the bridge numbers of the two factor links up to a constant error.