Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Three 20 minute research talks
Wenyuan Li (Northwestern), Estimating Reeb chords using microlocal sheaf theory
We show that, for closed Legendrians in 1-jet bundles, when there is a sheaf with singular support on the Legendrian, then (1) its self Reeb chords are bounded from below by half the sum of Betti numbers, and (2) the Reeb chords between itself and its Hamiltonian push off is bounded from below by Betti numbers when the $C^0$-norm of the Hamiltonian is small. I will show how to visualize Reeb chords/Lagrangian intersections in sheaf theory, and then explain the duality exact triangle and the persistence structure used in the proof. If time permits, I will state a conjecture on the relative Calabi-Yau structure that arises from the duality exact triangle.
Jakob Hedicke (Bochum), Lorentzian distance functions on the group of contactomorphisms
The notion of positive (non-negative) contact isotopy, defined by Eliashberg and Polterovich, leads to two relations on the group of contactomorphisms. These relations resemble the causal relations of a Lorentzian manifold. In this talk we will introduce a class of Lorentzian distance functions on the group of contactomorphisms, that are compatible with these relations. The Lorentzian distance functions turn out to be continuous with respect to the Hofer-norm of a contactomorphism defined by Shelukhin.
Johan Asplund (Uppsala), Simplicial descent for Chekanov-Eliashberg dg-algebras
In this talk we introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. We will discuss the result that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a descent (cosheaf) property with respect to a simplicial decomposition. Simplicial decompositions generalize the notion of Weinstein connected sum and there is in fact a one-to-one correspondence (up to Weinstein homotopy) between simplicial decompositions and so-called good sectorial covers. The motivation behind these results is the sectorial descent result for wrapped Fukaya categories by Ganatra-Pardon-Shende.