Abstract: The first example of a Lagrangian Barrier was introduced into symplectic geometry in 2001. It represents a symplectic rigidity phenomenon arising from necessary intersections with Lagrangian submanifolds which extend beyond mere topological considerations. Subsequently, numerous other instances of Lagrangian barriers have come to light.
In this joint work with Richard Hind and Yaron Ostrover, we present what appears to be the first illustration of Symplectic Barriers, a form of symplectic rigidity stemming from obligatory intersections of symplectic embeddings with symplectic submanifolds (and in particular not Lagrangian). In our work, we also tackle a question by Sackel–Song–Varolgunes–Zhu and provide bounds on the capacity of the ball after removing a codimension 2 hyperplane with a prescribed Kähler angle.
Abstract: On a compact surface of variable negative curvature, I will explain that the Poincaré series associated to the geodesic arcs joining two given points has a meromorphic continuation to the whole complex plane. Moreover, I will show that the value of Poincaré series at 0 can be expressed in terms of the linking of two Legendrian knots. I will also explain how this result extends when one considers geodesic arcs orthogonal to two fixed closed geodesics.
This is a joint work with N.V. Dang.
Abstract: In recent years, significant progress has been made in understanding the algebraic structure of the groups of area-preserving homeomorphisms of surfaces. In particular, in 2021 and 2022, Cristofaro-Gardiner, Humilière, Mak, Seyfaddini and Smith have used Heegaard Floer Homology to introduce new spectral invariants and prove the non-simplicity of several groups in the case of the disc and the sphere. In this talk, I will present a generalization of their results in higher genus. This is joint work with Cheuk Yu Mak.
