How should one estimate a signal, given only access to noisy
versions of the signal corrupted by unknown cyclic shifts? This
simple problem has surprisingly broad applications, in fields from
aircraft radar imaging to structural biology with the...
We show that every complete Riemannian manifold of finite volume
contains a complete embedded minimal hypersurface of finite volume.
This is a joint work with Gregory Chambers.
Lattices in higher rank simple Lie groups are known to be extremely
rigid. Examples of this are Margulis' superrigidity theorem, which
shows they have very few linear represenations, and Margulis'
arithmeticity theorem, which shows they are all...
In this talk we explain how billiard dynamics can be used to relate
a symplectic isoperimetric-type conjecture by Viterbo with an
80-years old open conjecture by Mahler regarding the volume product
of convex bodies. The talk is based on a joint work...
In this talk I will present a survey of some of the famous results
and examples in the classical theory of minimal and constant mean
curvature surfaces in R^3. The first examples of minimal surfaces
were found by Euler (catenoid) around 1741,...
In a series of works with Laszlo Szekelyhidi Jr. we pointed out
an unusual analogy between two problems in rather distant areas: a
long standing conjecture of Onsager in the theory of turbulence and
a (less known) critical regularity problem in...
In this talk I will survey recent advances on the existence theory
of minimal hypersurfaces from the variational point of view. I will
discuss what we know, what we do not know and point to future
directions. This is based on joint works with Andre...
Three fundamental factors determine the quality of a statistical
learning algorithm: expressiveness, optimization and
generalization. The classic strategy for handling these factors is
relatively well understood. In contrast, the radically
different...
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
confinement of waves, or eigenfunctions, to a small...
We will hear from two passionate creators of successful
mentoring programs in math for high school kids in educationally
challenged environments. They will give back-to-back talks about
their experiences and educational insights.
