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

Sebastian Haney (Columbia University) : Open enumerative mirror symmetry for lines in the mirror quintic

One of the earliest achievements of mirror symmetry was the prediction of genus zero Gromov-Witten invariants for the quintic threefold in terms of period integrals on the mirror. Analogous predictions for open Gromov-Witten invariants in closed Calabi-Yau threefolds can be formulated in terms of relative period integrals on the mirror, which govern extensions of variations of Hodge structure. I will discuss work in which I construct an immersed Lagrangian in the quintic which supports a family of objects in the Fukaya category mirror to vector bundles on lines in the mirror quintic, and deduce its open Gromov-Witten invariants from homological mirror symmetry. The domain of this Lagrangian immersion is a closed 3-manifold obtained by gluing together two copies of a cusped hyperbolic 3-manifold. The open Gromov-Witten invariants of the Lagrangian are irrational numbers valued in the invariant trace field of the hyperbolic pieces

Milica Ðukic (Uppsala University) : A deformation of the Chekanov-Eliashberg dg algebra using pseudoholomorphic annuli

We introduce an SFT-type invariant for Legendrian knots in R^3, which is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential includes components that count index zero pseudoholomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological component. We also describe a combinatorial way to compute the invariant from the Lagrangian projection

Yann Guggisberg (Utrecht University) : Instantaneous Hamiltonian displaceability and arbitrary squeezability for critically negligible sets

This talk will be about joint work with Fabian Ziltener in which we show that a compact n-rectifiable subset of R^2n with vanishing n-Hausdorff measure can be displaced from itself by a Hamiltonian diffeomorphism arbitrarily close to the identity. This has the consequence that such a set can be arbitrarily symplectically squeezed, i.e. embedded into any neighborhood of the origin in R^2n