Mathematics Colloquia and Seminars

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We introduce a mod p analogue of the Mumford—Tate conjecture, which governs the p-adic monodromy of families of mod p abelian varieties. We will also introduce mod p variants of two unlikely intersections problems: the Ax—Schanuel conjecture and the André—Oort conjecture. We will see how the three conjectures are extremely closely entangled — a phenomenon only seen in positive characteristic. I will talk about my previous work on the three conjectures for GSpin Shimura varieties. But time permitting, we will go much further than that.