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...
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...
Motivated by counting problems for closed geodesics on
hyperbolic surfaces, I will present a family of new results
describing the dynamics of mapping class groups on Teichmüller
spaces and spaces of closed curves of closed surfaces.
