David Hansen ( Columbia )
How to filter a modified vector bundle for fun and profit

Abstract: Much of classical p-adic Hodge theory can be reinterpreted "geometrically" on the Fargues-Fontaine curve, in terms of vector bundles and modifications of vector bundles. After recalling this dictionary between "classical" and "geometric" p-adic Hodge theory, I'll describe some very general results which (roughly) allow one to put a canonical filtration (or several such filtrations) on a modification of vector bundles, both pointwise and (more subtly) in families. I'll also explain some particular applications of these results to a conjecture of Harris on the cohomology of moduli spaces of local shtukas, and to the geometry of p-adic period domains.