Zoom link:  https://princeton.zoom.us/j/97126136441

Passcode: the three digit integer that is the cube of the sum of its digits

Given a K3 surface X over a number field K, we prove that the set of primes of K where the geometric Picard rank jumps is infinite, assuming that X has everywhere potentially good reduction. This result is formulated in the general framework of GSpin Shimura varieties and I will explain other applications to abelian surfaces. I will also discuss applications to the existence of rational curves on K3 surfaces.

The results in this talk are joint work with Ananth  Shankar, Arul Shankar and Yunqing Tang.