Mohan Swaminathan, Ben Wormleighton, & Jonathan Zung

Mohan Swaminathan, Ben Wormleighton, & Jonathan Zung

Three 20 Minute Research Talks

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Mohan Swaminathan (Princeton)
Title: Super-rigidity and bifurcations of embedded curves in Calabi-Yau 3-folds

Abstract: 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 (WashU)
Title: Lattice formulas for rational SFT capacities of toric domains

Abstract: 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)
Title: Reeb flows transverse to foliations

Abstract: Eliashberg and Thurston showed that C^2 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.