Predicting the future for a Hamiltonian dynamical system is an
old and notoriously difficult problem. I will present some evidence
however that in the simplest situation where one iterates an area
preserving map on the 2-disk, solutions to an...
Deift--Simon and Poltoratskii--Remling proved upper bounds on
the measure of the absolutely continuous spectrum of Jacobi
matrices. Using methods of classical approximation theory, we give
a new proof of their results, and generalize them in several...
The correspondence between homotopy types and higher categorical
analogs of groupoids which was first conjectured by Alexander
Grothendieck naturally leads to a view of mathematics where sets
are used to parametrize collections of objects without...
This is a report on some joint work with Mark Reeder and
Jiu-Kang Yu. I will review the theory of parahoric subgroups and
consider the induced representation of a one-dimensional character
of the pro-unipotent radical. A surprising fact is that this...
In Greek religion, the encounter between mortals and gods was
dominated by fear. The belief in the power of gods was based on
experience and enhanced through rituals. Cult regulations,
narratives of punitive miracles, confession inscriptions,
and...
We study families of filtered phi-modules associated to families
of p-adic Galois representations as considered by Berger and
Colmez. We show that the weakly admissible locus in a family of
filtered phi-modules is open and that the groupoid of...
A "proof assistant" is a software package comprising a validity
checker for proofs in a particular logic, accompanied by
semi-decision procedures called "tactics" that assist the
mathematician in filling in the easy parts of the proofs. I
will...
The local Langlands conjecture (LLC) seeks to parametrize
irreducible smooth representations of a p-adic group G in terms of
Weil-Deligne parameters. Bernstein's theory describes the category
of smooth representations of G in terms of points on a...
