Christopher Daw, Institut des Hautes Etudes Scientifiques (IHES)
"Unlikely intersections in Shimura varieties"
Abstract: Many important problems in arithmetic geometry can be interpreted as questions regarding unlikely intersections. The Zilber-Pink conjecture on mixed Shimura varieties is a vast example. In this talk, we will focus on a special case --- the Andr\’e-Oort conjecture --- which is now known to hold for many Shimura varieties thanks to new techniques from model theory. We will explain these techniques, as well as others from number theory, algebraic geometry and ergodic theory. To introduce the topic, we will discuss two analogues of the Andr\'e-Oort conjecture --- Lang's conjecture on roots of unity, and the Manin-Mumford conjecture on abelian varieties.
Refreshments will be served in MC 5403 at 3:30 pm.