Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Three 20 minute research talks
Mohan Swaminathan (Princeton), Super-rigidity and bifurcations of embedded curves in Calabi-Yau 3-folds
I will describe my recent work, joint with Shaoyun Bai, which studies a class of bifurcations of moduli spaces of embedded pseudo-holomorphic curves in symplectic Calabi-Yau 3-folds and their associated obstruction bundles. As an application, we are able to give a direct definition of the Gopakumar-Vafa invariant in a special case.
Ben Wormleighton (Washington University), Lattice formulas for rational SFT capacities of toric domains
Siegel has recently defined ‘higher’ symplectic capacities using rational SFT that obstruct symplectic embeddings and behave well with respect to stabilisation. I will report on joint work with Julian Chaidez that relates these capacities to algebro-geometric invariants, which leads to computable, combinatorial formulas for many convex toric domains.
Jonathan Zung (Princeton), Reeb flows transverse to foliations
Eliashberg and Thurston showed that taut foliations on 3-manifolds can be approximated by tight contact structures. I will explain a new approach to this theorem which allows one to control the resulting Reeb flow and hence produce many hypertight contact structures. Along the way, I will explain how harmonic transverse measures may be used to understand the holonomy of foliations.