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

Triangulated categories play an important role in symplectic topology. The aim of this talk is to explain how to combine triangulated structures with persistence module theory in a geometrically meaningful way. The guiding principle comes from the...

Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The...

Viterbo conjectured that a normalized symplectic capacity, on convex domains of a given volume, is maximized for the ball. A stronger version of this conjecture asserts that all normalized symplectic capacities agree on convex domains. Since...

I will start by explaining Takahashi's homological mirror symmetry (HMS) conjecture regarding invertible polynomials, which is an open string reinterpretation of Berglund-Hubsch-Henningson mirror symmetry. In joint work with A. Polishchuk, we...

The Arnold conjecture about fixed points of Hamiltonian diffeomorphisms was partly motivated by the celebrated Poincare-Birkhoff fixed point theorem for an area-preserving homeomorphism of an annulus in the plane. Despite the fact that the Arnold...

This talk reports on joint work with Maria Bertozzi, Tara Holm, Emily Maw, Grace Mwakyoma, Ana Rita Pires, and Morgan Weiler on a WiSCon project to investigate the embedding capacity function of the one-point blow up of ?P2. We found three new...

This talk will discuss a new algebraic structure called triangulated persistence category (TPC). It combines the triangulated category structure with the persistence module structure. This algebraic structure can be used to associate a metric...

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...

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...

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...