Lusztig's theory of character sheaves for connected reductive
groups is one of the most important developments in representation
theory in the last few decades. In this talk, we will describe a
construction which extends this "depth zero" picture to...
We develop on a new strategy based on point-set topology, which
allows us to produce a purely p-adic statement for the
crystallinity properties of rigid flat connections.
Let X be a proper, smooth rigid space and G a commutative rigid
group. We study the relationship between G-representations of the
fundamental group of X and G-Higgs bundles on X. This is joint work
with Ben Heuer and Mingjia Zhang.
Given a family of motives, the de Rham realization (a certain
vector bundle with integrable "Gauss-Manin" connection) can be
compared to the crystalline realizations for various primes p, but
the resulting Frobenius structures cannot be directly...
