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

It is well-known that the geodesic flow on ellipsoids of revolution is integrable. In joint work with Ferreira and Vicente, we used this fact to obtain a symplectomorphism between the unit disk bundle of such an ellipsoid without fiber and a toric...

In this talk, we will explore the relationship between the geometry and topology of a complexity-one four-manifold and the combinatorial data that encode it. We will use a generators-and-relations description for the even part of the equivariant...

We define the systolic $S^1$-index of a convex body as the Fadell–Rabinowitz index of the space of centralized generalized systoles associated with its boundary. We show that this index is a symplectic invariant. Using the systolic $S^1$-index, we...

Given a finite collection of disjoint Lagrangian circles on a symplectic surface satisfying some area constraints, Cristofaro-Gardiner, Humilière, Mak, Seyfaddini and Smith define a link spectral invariant, by computing the Lagrangian Floer homology...

In algebraic geometry, the Ceresa cycle provided one of the first examples of a nullhomologous cycle which is not algebraically trivial. I will explain how one can obtain a mirror statement about the Lagrangian Ceresa cycle, a nullhomologous...

The double bubble plumbing, first studied by Smith and Wemyss, is a Stein neighborhood of two Lagrangian 3-spheres intersecting cleanly along an unknotted circle in some 6-dimensional symplectic manifold. Depending on the identification of the...

The parametrised Whitehead torsion is an invariant of families of manifolds, and can be viewed as a map to an algebraic K-theory space. A strong version of the nearby Lagrangian conjecture says that when applied to families of closed exact...

We will explore certain $C^0$-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is related to the Rokhlin property of the group of...

I will describe and argue the existence of contact non-squeezing phenomena in contact lens spaces and in strongly orderable prequantizations.

The proof is based on the construction of contact capacities coming from spectral selectors defined on the...

We will outline the proof of an intersection result between embedded Lagrangian tori and certain 1 parameter families of product Lagrangian tori in the 4 dimensional symplectic cylinder. The theorem can be applied to give new computations of the...