Diophantine Results for Shimura Varieties
Welcoming remarks: Dean Mark Giesbrecht (University of Waterloo)
Laudation: Professor Peter Sarnak (Institute for Advanced Study and Princeton University)
Ostrowski Lecture: Professor Jacob Tsimerman (University of Toronto)
Shimura Varieties are higher dimensional analogues of modular curves, and they play a foundational role in modern number theory. The most familiar Shimura varieties are the moduli spaces of Abelian varieties, and in this context we have a wealth of diophantine results, both in the number field and function field setting: Finiteness of S-rational points, the Tate conjecture, the Shafarevich conjecture, semisimplicity of Galois representations, and others. These results constitute a blueprint for what we expect to be true in other settings but is largely out of reach.
DC1302