Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Oğuz Şavk (Boğaziçi University), Classical and new plumbings bounding contractible manifolds and homology balls

A central problem in low-dimensional topology asks which homology 3-spheres bound contractible 4-manifolds and homology 4-balls. In this talk, we address this problem for plumbed 3-manifolds and we present the classical and new results together. Along the way, we touch symplectic geometry by using the classical results of Eliashberg and Gompf. Our approach is based on Mazur’s famous argument which provides a unification of all results.

Irene Seifert (Heidelberg University), Periodic delay orbits and the polyfold IFT

Differential delay equations arise very naturally, but they are much more complicated than ordinary differential equations. Polyfold theory, originally developed for the study of moduli spaces of pseudoholomorphic curves, can help to understand solutions of certain delay equations. In my talk, I will show an existence result about periodic delay orbits with small delay. If time permits, we can discuss possible further applications of polyfold theory to the differential delay equations. This is joint work with Peter Albers.

Hang Yuan (Stony Brook University), Disk counting via family Floer theory

Given a family of Lagrangian tori with full quantum corrections, the non-archimedean SYZ mirror construction uses the family Floer theory to construct a non-archimedean analytic space with a global superpotential. In this talk, we will first briefly review the construction. Then, we will apply it to the Gross’s fibrations. As an application, we can compute all the non-trivial open GW invariants for a Chekanov-type torus in $CP^n$ or $CP^r \times CP^{n-r}$. When $n = 2$, $r = 1$, we retrieve the previous results of Auroux an Chekanov-Schlenk without finding the disks explicitly. It is also compatible with the Pascaleff-Tonkonog’s work on Lagrangian mutations.