Ascending surfaces, complex curves, and knot Floer homology- Kyle Hayden (Columbia University)
Abstract: Ascending surfaces are a natural class of surfaces in certain symplectic 4-manifolds that behave like complex curves, but they are much more flexible. I'll present a key structural result about these surfaces and highlight two applications: one to the study of complex curves, the other to recent results of Juhasz-Miller-Zemke regarding the transverse invariant in knot Floer homology.
Right-veering open books and the Upsilon invariant- Diana Hubbard (Brooklyn College, CUNY)
Abstract: Fibered knots in a three-manifold Y can be thought of as the binding of an open book decomposition for Y. A basic question to ask is how properties of the open book decomposition relate to properties of the corresponding knot. In this talk I will describe joint work with Dongtai He and Linh Truong that explores this: specifically, we can give a sufficient condition for the monodromy of an open book decomposition of a fibered knot to be right-veering from the concordance invariant Upsilon. I will discuss an application of this work to the Slice-Ribbon conjecture.
GRID invariants obstruct decomposable Lagrangian cobordisms- C.-M. Michael Wong (Louisiana State Unversity)
Abstract: Ozsvath, Szabo, and Thurston defined several combinatorial invariants of Legendrian links in the 3-sphere using grid homology, which is a combinatorial version of link Floer homology. These, collectively called the GRID invariants, are known to be effective in distinguishing some Legendrian knots that have the same classical invariants. In this talk, we show that the GRID invariants provide an obstruction to the existence of decomposable Lagrangian cobordisms between Legendrian links. This obstruction is stronger than the obstructions from the Thurston-Bennequin and rotation numbers, and is closely related to a recent result by Golla and Juhasz. This is joint work with John Baldwin and Tye Lidman.