IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry

Fukaya category for Landau-Ginzburg orbifolds and Berglund-Hübsch homological mirror symmetry for curve singularities

Cheol-Hyun Cho
Seoul National University
September 21, 2020
For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category based on wrapped Fukaya category of its Milnor fiber together with monodromy information. It is analogous to the variation operator in singularity theory. As an application, we formulate a complete version of Berglund-Hübsch homological mirror symmetry and prove it for two variable cases.

Reeb dynamics in dimension 3 and broken book decompositions

Vincent Colin
Université de Nantes
September 11, 2020
In a joint work with Pierre Dehornoy and Ana Rechtman, we prove that on a closed 3-manifold, every nondegenerate Reeb vector field is supported by a broken book decomposition. From this property, we deduce that in dimension 3 every nondegenerate Reeb vector field has either 2 or infinitely periodic orbits and that on a closed 3-manifold that is not graphed, every nondegenerate Reeb vector field has positive topological entropy.

Hamiltonian classification and unlinkedness of fibres in cotangent bundles of Riemann surfaces

Georgios Dimitroglou Rizell
Uppsala University
September 4, 2020
In a joint work with Laurent Côté we show the following result. Any Lagrangian plane in the cotangent bundle of an open Riemann surface which coincides with a cotangent fibre outside of some compact subset, is compactly supported Hamiltonian isotopic to that fibre. This result implies Hamiltonian unlinkedness for Lagrangian links in the cotangent bundle of a (possibly closed Riemann surface whose components are Hamiltonian isotopic to fibres.