Title: Fixed Q under the reverse operation in the RSK correspondence  Abstract: The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted $P$ (insertion) and $Q$ (recording). It has been an open problem to demonstrate       where $w^r$ is the reverse permutation

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

Title: Infinitely many Lagrangian Tori in Milnor fibers constructed via Lagrangian Fillings of Legendrian links Abstract: One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings

Title: The homotopy type of a finite 2-complex with non-minimal Euler characteristic Abstract: Two presentations for a group G which have the same deficiency are called exotic if the corresponding presentation complexes are not homotopy equivalent. The first examples of exotic presentations were found by Dunwoody and Metzler in the 1970s but, owing to the difficulty of

Title: Mutations of reflections and existence of pseudo-acyclic orderings for type An   Abstract: In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix representation of these reflections is determined by a linear ordering

Title: Some Link Detection ResultsAbstract: A central question in low dimensional topology is; how can we distinguish links? In this talk I will discuss various classical invariants which can help us do so, as well as the stronger invariant Knot Floer homology and, time permitting, annular Khovanov homology. Indeed, we will see that these latter