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...
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...
The classical Dvoretzky theorem asserts that for every integer
k>1 and every target distortion D>1 there exists an integer
n=n(k,D) such that any
n-dimensional normed space contains a subspace of dimension k that
embeds into Hilbert space with...
Using a version of cylindrical contact homology on the
complement of some Reeb orbits in a 3-dimensional contact manifold
we will deduce that the existence of closed Reeb orbits with
certain topological/dynamical properties implies the existence
of...
