Special Year Seminar - Math

In this talk I will introduce a bi-\bar{Q}-structure on Shimura varieties, propose a hyperbolic analytic subspace conjecture (analogue of Wüstholz’s analytic subgroup theorem in this context), and explain its consequence on quadratic relations...

Every o-minimal structure determines a collection of "tame" or "definable" subsets of $bbR^n$. We can then ask about the fragment of complex geometry present in the structure: Which holomorphic functions are definable, and which spaces are cut out...

I will discuss questions pertaining to geometric unlikely intersections and transcendence in the setting of torii in positive characteristic. This is based on work in progress joint with Anup Dixit, Philip Engel, and Ruofan Jiang.