Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Three 20 minute research talks
Jean-Philippe Chassé (UdeM)
Title: Convergence and Riemannian bounds on Lagrangian submanifolds
Abstract: Recent years have seen the appearance of a plethora of possible metrics on spaces of Lagrangian submanifolds. Indeed, on top of the better-known Lagrangian Hofer metric and spectral norm, Biran, Cornea, and Shelukhin have constructed families of so-called weighted fragmentation metrics on these spaces. I will explain how — under the presence of bounds coming from Riemannian geometry — all these metrics behave well with respect to the set-theoretic Hausdorff metric.
Leo Digiosia (Rice)
Title: Cylindrical contact homology of links of simple singularities
Abstract: In this talk we consider the links of simple singularities, which are contactomoprhic to $S^3/G$ for finite subgroups $G$ of $SU(2,C)$. We explain how to compute the cylindrical contact homology of $S^3/G$ by means of perturbing the canonical contact form by a Morse function that is invariant under the corresponding rotation subgroup. We prove that the ranks are given in terms of the number of conjugacy classes of $G$, demonstrating a form of the McKay correspondence. We also explain how our computation realizes the Seifert fiber structure of these links.
Rima Chatterjee (Cologne)
Title: Cabling of knots in overtwisted contact manifolds
Abstract: Knots associated to overtwisted manifolds are less explored. There are two types of knots in an overtwisted manifold – loose and non-loose. Non-loose knots are knots with tight complements whereas loose knots have overtwisted complements. While we understand loose knots, non-loose knots remain a mystery. The classification and structure problems of these knots vary greatly compared to the knots in tight manifolds. Especially we are interested in how satellite operations on a knot in overtwisted manifold changes the geometric property of the knot. In this talk, I will discuss under what conditions cabling operation on a non-loose knot preserves non-looseness. This is a joint work with Etnyre, Min and Mukherjee.