## PATCH day November 3 – Bourgeois and Lecuona

On Thursday, November 3, the regional PATCH seminar takes place at Bryn Mawr. The talks will be held in the Park Science Building, room 336. The two speakers are Frederic Bourgeois of Universite Libre de Bruxelles and Ana Lecuona of Penn State University.

Bourgeois will speak at 4:00, on:

Title: $S^1$-equivariant symplectic homology and contact homology

Abstract: In this joint work with Alexandru Oancea, we construct an $S^1$-equivariant version of symplectic homology. We then describe various algebraic structures as well as a simpler computational approach for this invariant. Finally, we sketch the proof that this invariant coincides with (linearized) contact homology. The advantage of the first invariant is that transversality results can be established for large classes of symplectic manifolds, while for contact homology, the corresponding results would rely on the recent theory of polyfolds.

Lecuona will speak at 5:15, on:

Title: Montesinos knots and the slice-ribbon conjecture

Abstract: The slice-ribbon conjecture states that a knot in the three sphere is the boundary of an embedded disc in the four ball if and only if it bounds a disc in the sphere which has only ribbon singularities. This conjecture was proposed by Fox in the early 70s. There doesn´t seem to be any conceptual reason for it to be true, but large families of knots (i.e. pretzel knots, two bridge knots) satisfy it. In this seminar we will prove that the conjecture remains valid for a large family of Montesinos knots. The proof is based on Donaldson’s diagonalization theorem for definite four manifolds.

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