I will discuss how to build small symplectic caps for contact
manifolds as a step in building small closed symplectic
4-manifolds. As an application of the construction, I will give
explicit handlebody descriptions of symplectic embeddings of...
I'll explain joint work in progress with Abbondandolo and Kang
concerning the Clarke dual action functional of convex domains and
pseudoholomorphic planes. In dimension 4, I'll explain applications
to the knot types of periodic Reeb orbits.
A recent line of work has shown a surprising connection between
multicalibration, a multi-group fairness notion, and
omniprediction, a learning paradigm that provides simultaneous loss
minimization guarantees for a large family of loss functions...
My plan is to explain how complex projective spaces can be
identified with components of totally elliptic representations of
the fundamental group of a punctured sphere into PLS(2,R). I will
explain how this identification realizes the pure mapping...
Studying symplectic structures up to deformation equivalences is
a fundamental question in symplectic geometry. Donaldson asked:
given two homeomorphic closed symplectic four-manifolds, are they
diffeomorphic if and only if their stabilized...
Etale cohomology of Fp-local systems does not behave nicely on
general smooth p-adic rigid-analytic spaces; e.g., the
Fp-cohomology of the 1-dimensional closed unit ball is
infinite.
However, it turns out that the situation is much better if
one...
Coboundary expansion and cosystolic expansion are
generalizations of edge expansion to hypergraphs. In this talk, we
will first explain how the generalizations work. Next we will
motivate the study of such hypergraphs by looking at their...
The Breuil-Mezard Conjecture predicts the existence of
hypothetical "Breuil-Mezard cycles" that should govern congruences
between mod p automorphic forms on a reductive group G. Most of the
progress thus far has been concentrated on the case G = GL...
Translational tiling is a covering of a space (such as Euclidean
space) using translated copies of one building block, called a
"translational tile'', without any positive measure
overlaps.
Can we determine whether a given set is a translational...
The dynamics associated with mechanical Hamiltonian flows with
smooth potentials that include sharp fronts may be modeled, at the
singular limit, by Hamiltonian impact systems: a class of
generalized billiards by which the dynamics in the domain’s...
