Video Lectures

The notion of positive (non-negative) contact isotopy, defined by Eliashberg and Polterovich, leads to two relations on the group of contactomorphisms. These relations resemble the causal relations of a Lorentzian manifold. In this talk we will...

We show that, for closed Legendrians in 1-jet bundles, when there is a sheaf with singular support on the Legendrian, then (1) its self Reeb chords are bounded from below by half the sum of Betti numbers, and (2) the Reeb chords between itself and...

It was suggested over thirty years ago that microscopic black holes can exponentially enhance the decay rate of a metastable false vacuum. The interest in this phenomenon has revived recently due to its possible phenomenological relevance for the...

Computing non-protected observables in AdS/CFT in presence of RR background fluxes is notoriously hard. For the spectrum of integrable backgrounds, Bethe ansatz techniques provide a framework for doing so. For correlation functions, the hexagon...

We discuss a local to global profinite principle for being a commutator in some arithmetic groups. Specifically we show that SL2(Z) satisfies such a principle, while it can fail with infinitely many exceptions for SL2(Z[1/p]). The source of the...

Several different areas of group theory, topology, and geometry have led to the study of the action of Aut(Fn)—the automorphism group of the free group on n generators—on Hom(Fn,G) when G is either finite, compact or a simple Lie group. We will...

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...

Expander graphs are sparse and yet well-connected graphs. Several applications in theoretical computer science require explicit constructions of expander graphs, sometimes even with additional structure. One approach to their construction is to...

Localization is an important construction in algebra and topology that allows one to study global phenomena a single prime at a time. Flexibilization is an operation in symplectic topology introduced by Cieliebak and Eliashberg that makes any two...