School of Mathematics

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...

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...

I will introduce a new model of randomly agitated equations. I will focus on the finite finite dimensional approximations (analogous to Galerkin approximations) and the two-dimensional setting. I will discuss number of properties of the models...

This is joint work with Agustin Moreno and Dayung Koh. The restricted three-body problem is invariant under various antisymplectic involutions. These real structures give rise to the notion of symmetric periodic orbits which simultaneously have a...

Joint IAS/Princeton University Number Theory Seminar Topic: Abelian varieties not isogenous to Jacobians Speaker: Jacob Tsimerman Affiliation: University of Toronto Date: December 01, 2021 Katz and Oort raised the following question: Given an...