Speaker: Dr. Ruofan Jiang (UC Berkeley)

Time: 14:15-15:15 & 15:30-16:30  August 20, 2026 (Thursday)

Inviter: Prof. Hongjie Yu (MCM, CAS)

Place: MCM110

Titles & Abstracts:

Talk 1: Mumford-Tate conjecture and unlikely intersection in char p

For an abelian variety A over a number field, the Mumford-Tate group MT(A) is the monodromy group of its Hodge structure. It is conjectured that MT(A) tensor Q_p is the neutral component of the p-adic étale monodromy group G_p(A).

I will talk about an analogue of the conjecture in char p, and show that it is equivalent to an unlikely intersection problem of Ax-Lindemann type. Time permitting, I will talk about one of the following two topics: André-Oort conjecture in char p, or p-adic Hodge loci.

Talk 2: Integral cycles on reductions of K3 surfaces

I give an application of mod p Mumford-Tate in the last talk:

Given an ordinary K3 surface X over a char p global field K, we show that for an arbitrary infinite collection M of positive integers coprime to p, there are infinitely many places of K modulo which the reduction of X has an extra line bundle of self-intersection number lying in M.

The main input is an algebraization result established via mod p Mumford-Tate for Spin Shimura varieties, which reduces us to a situation where we apply Diophantine approximation to the Picard group.

This is a forthcoming joint work with Ananth Shankar.