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

Baptiste Serraille (ETH Zürich) On a Linear Combination of Link Spectral Invariants on the Sphere:

Link spectral invariants and their homogenizations have been defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim Trifa, we define a linear combination of such quasimorphism and show that it vanishes on the stabilizer of the equator in $S^2$. We will discuss this result and how it relates to the, still open, equator conjecture.

Spencer Cattalani (Stony Brook University) Ahlfors Currents and Symplectic Non-hyperbolicity: 

Rational curves are one of the main tools in symplectic geometry and provide a bridge to algebraic geometry. Complex lines are a more general class of curve that has the potential to connect symplectic and complex analytic geometry. These curves are non-compact, which presents a serious difficulty in understanding their symplectic aspects. In this talk, I will explain how Ahlfors currents can be used to resolve this difficulty and produce a theory parallel to that of rational curves. In particular, Ahlfors currents can be constructed via a continuity method, they control bubbling of holomorphic curves, and they form a convex set.

Giovanni Ambrosioni (ETH Zürich) Approximability for Lagrangian Submanifolds:

In this talk I will introduce a new notion of approximability for metric spaces that can be seen as a categorification of a concept introduced by Turing for metric groups and as a generalization of total-boundedness. I will explain how recent technological advances in symplectic topology and persistence category theory allow us to talk about approximablity of spaces of Lagrangian submanifolds and discuss applications to rigidity and complexity of Lagrangians, as well as potential relations to open problems in Lagrangian topology. This talk is based on joint work with Paul Biran and Octav Cornea.