Previous Special Year Seminar

In this talk, I will explain how the Ruelle invariant of a symplectomorphism and the Ruelle invariant of a Reeb flow are related via the open book construction. As an application, I will construct examples of Reeb flows on the sphere that are...

Floer homology is a fundamental construction relating dynamical properties of Hamiltonian flows on symplectic manifolds to the topology of the manifold. Although this construction is global in nature, when the Hamiltonian flow is supported on a...

In this talk, I will define the Ruelle invariant of a measure preserving flow equipped with a symplectic cocycle. This is a natural dynamical quantity that measures a spacetime averaged rotation of the cocycle along the flow. I will then discuss the...

Complexity of the geometry, randomness of the potential, and many other irregularities of the system can cause powerful, albeit quite different, manifestations of localization, a phenomenon of sudden confinement of waves, or eigenfunctions, to a...

I will explain a proof of a joint with D. Alvarez-Gavela and D. Nadler theorem which allows to make a Lagrangian submanifold transverse to a given Lagrangian distribution in exchange for making them piecewise smooth with canonical singularities...