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.
An old open question in symplectic geometry asks whether all
normalised symplectic capacities coincide for convex domains in the
standard symplectic vector space. I will show that this question
has a positive answer for smooth convex domains which...
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...