Title: The non-orientable 4-ball genus of torus knots Abstract: The non-orientable 4-ball genus of a knot $K$ in $S^3$ is the minimal first Betti number of any smoothly embedded non-orientable surface in $B^4$ bounded by K. This is the non-orientable analog of the 4-ball genus of $K$ (i.e. the minimal genus of any smooth orientable surface

Title: On Anosovity, divergence and bi-contact surgery Abstract: I will revisit the relation between Anosov 3-flows and invariant volume forms, from a contact geometric point of view. Consequently, I will give a contact geometric characterization of when a flow with dominated splitting is Anosov based on its divergence, as well as a Reeb dynamical interpretation

Title: Detection results in link Floer homology  Abstract: In this talk I will briefly describe link Floer homology toolbox and its usefulness. Then I will show how link Floer homology can detect links with small ranks, using a rank bound for fibered links by generalizing an existing result for knots. I will also show that stronger

Title: Symplectic fillings of lens spaces Abstract: Many contact 3-manifolds arise as boundaries of symplectic 4-manifolds, and we are often interested in the filling problem for a given contact 3-manifold.  That is, how many symplectic 4-manifolds have the given contact boundary?  This problem has previously been solved for standard contact structures on lens spaces.  We use

Title: Slice links and smooth 4-manifolds Abstract: We vary the trace embedding lemma in order to prove results about smooth, closed, simply connected 4-manifolds, studying smoothly slice links in them. We focus on homotopy 4-spheres, which are potential counterexamples to the smooth 4-dimensional Poincaré conjecture. In particular, we split them, as for exotic R^4's,  in large and