Speaker: Prof. Hui Gao (SUSTech)

Title: Galois representations over convergent de Rham period ring

Time: 15:10-16:10  May 22, 2026 (Friday)

Place: MCM110

Abstract: Inside Fontaine's de Rham period ring B_dR^+, there is a convergent subring which is exactly the (un-completed) stalk at the de Rham point of the Fargues--Fontaine curve. We study Galois representations over this convergent subring, and compare with the classical theory over B_dR^+. Some tools in p-adic differential equations, in particular, the p-adic non-Liouville conditions will naturally appear. This is joint work with Yupeng Wang.

Speaker: Prof. Heng Du (Tsinghua University)

Title: From p-adic Hodge theory to relative shtukas—and back

Time: 16:45-17:45  May 22, 2026 (Friday)

Place: MCM110

Abstract: The category of p-adic local shtukas was introduced by Scholze as a mixed-characteristic analog of Drinfeld’s shtukas. Its formulation was made possible by several major developments in p-adic Hodge theory, including Scholze’s theory of perfectoid spaces and diamonds, the foundational work of Fargues and Fontaine on the Fargues–Fontaine curve, and the framework of relative p-adic Hodge theory developed by Kedlaya and Liu. Since their introduction, p-adic local shtukas have played a central role in recent progress toward the geometrization of the local Langlands program. In this talk, I will explain how ideas from this circle of developments can also be brought back to p-adic Hodge theory. In particular, I will show that reasonable categories of arithmetic Z_p-local systems can be embedded, in a compatible way, into the category of relative shtukas. As an application, I will discuss how this viewpoint leads to new insights into the relative p-adic monodromy conjecture.