|Location:||MSRI: Simons Auditorium, Online/Virtual|
To receive a link to participate remotely, please subscribe to our weekly Math Lecture Announcements email list.
It is often the case that in concrete Diophantine problems it is not enough to show that the rational points on a variety are algebraically degenerate; one also needs to describe their Zariski closure. In arithmetic questions such as Vojta's conjecture and the Bombieri-Lang conjecture, this Zariski closure is referred to as the special set. In this talk I will explain some techniques based in omega-integrality to describe the special set in Diophantine conjectures over number fields and function fields, and to prove some instances of these conjectures in the function field case.
Arithmetic Conjectures and their Special Sets