Organizers: Kyle Hayden and Lev Tovstopyat-Nelip
Time and location: Fridays 12pm, Maloney 560 (tentative schedule)
About: This is a weekly seminar run by graduate students. The talks should be related to Floer homology, Khovanov homology, or contact/symplectic geometry.
|Nov 3||Lev||A characterization of the transverse invariant in knot Floer homology|
|Nov 10||Kyle||The symplectic isotopy problem|
|Nov 17||Melissa||Tangle Floer homology and bordered invariants|
Titles, descriptions, and references:
I'll review the braid definition of the transverse invariant and prove that it is characterized in terms of an Alexander filtration induced by the binding. Along the way I'll prove a non vanishing result. If time permits, I'll use the characterization to define an invariant of transverse knots in lens spaces using grid diagrams.
The symplectic isotopy conjecture states that every smooth symplectic surface in CP2 is symplectically isotopic to a complex algebraic curve. We'll review the setup and history of the problem, a key special case due to Gromov, and a recent theorem of Laura Starkston that recasts the problem as an existence statement about certain embedded Lagrangian disks.
Tangle Floer homology is a cut-and-paste reconstruction of knot Floer homology. It assigns dgas to the ends of a tangle and an A∞-module to the the tangle. The box tensor product represents gluing the ends of different tangles together, recovering knot Floer homology from tangle Floer homology. The goal is to get a glimpse of the world of bordered invariants, so we'll focus on introducing the main players in bordered constructions, starting from definitions of algebraic objects like dgas and A∞ structures. Time permitting, we may discuss what algebraically happens when we view a link as a tangle closure rather than the composition of multiple tangles.