University of Calgary

We prove a positive characteristic analogue of the classical result that the centralizer of a nonconstant differential operator in one variable is commutative. This leads to a new, short proof of that classical characteristic zero result, by reduction modulo p. This is joint work with Justin Desrochers available at https://arxiv.org/abs/2201.04606.

In this talk, I will describe a construction of a $p$-adic L-function attached to a triple of $p$-adic Coleman families of cusp forms.  This function interpolates algebraic parts of special values of Garrett triple product L-functions at balanced triples of weights.  Our construction is complementary to that of Harris and Tilouine which treats the case of unbalanced weights.

Modern differential geometry is the art of the abstract that can be pictured. Continuum mechanics is the abstract description of concrete material phenomena. Their encounter, therefore, is as inevitable and as beautiful as the proverbial chance meeting of an umbrella and a sewing machine on a dissecting table. In this rather non-technical and lighthearted talk, some of the surprising connections between the two disciplines will be explored with a view at stimulating the interest of applied mathematicians.