In this talk, I'll show that the most natural low-degree test
for polynomials over finite fields is ``robust'' in the high-error
regime for linear-sized fields. This settles a long-standing open
question in the area of low-degree testing, yielding...
Although there are several ways to ''choose a compact hyperbolic
surface at random'', putting the Weil-Petersson probability measure
on the moduli space of hyperbolic surfaces of a given topology is
certainly the most natural. The work of M...
Although there are several ways to ''choose a compact hyperbolic
surface at random'', putting the Weil-Petersson probability measure
on the moduli space of hyperbolic surfaces of a given topology is
certainly the most natural. The work of M...
Chen and Ruan constructed symplectic orbifold Gromov-Witten
invariants more than 20 years ago. In ongoing work with Alex
Ritter, we show that moduli spaces of pseudo-holomorphic curves
mapping to a symplectic orbifold admit global Kuranishi
charts...
An inertial manifold is a positively invariant smooth
finite-dimensional manifold which contains the global attractor and
which attracts the trajectories at a uniform exponential rate. It
follows that the infinite-dimensional dynamical system is...
It is conjectured that every Reeb flow on a closed
three-manifold has either two, or infinitely many, simple periodic
orbits. I will survey what is currently known about this
conjecture. Then, I will try to explain some of the key ideas
behind...
Ratner's landmark equidstribution results for unipotent flows
have had dramatic applications in many mathematical areas. Recently
there has been considerable progress in the long sought for goal of
getting effective equidistribution results for...
