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

Given a Morse-Smale pair on a manifold M, it is possible to entirely recover its fundamental group in a combinatorial manner. We call this construction the Morse fundamental group. Motivated by a similar construction of a « Floer fundamental group »...

Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of a group action, is whether a certain Lagrangian is equivariantly displaceable, that is by a...

The Birkhoff attractor is a closed invariant subset associated with any dissipative twist map of the annulus (of dimension 2), which was introduced by Birkhoff in 1932. We will see that it can be generalized to higher dimensions using tools from...

The symplectic area of a Lagrangian submanifold L in a symplectic manifold is defined as the minimal positive symplectic area of a smooth 2-disk with boundary on L. A Lagrangian torus is called extremal if it maximizes the symplectic area among all...

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...

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...

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...

The chord conjecture, due initially to Arnol'd in the case of the standard contact three-sphere, asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. This...

Given a local system on a complex algebraic variety, what are the subvarieties on which the monodromy drops? The talk will discuss these monodromy special loci, a natural generalisation of (the positive period dimension components of) the Hodge loci...

We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is Hamiltonian isotopic to a special...