# The Ax Conjecture and Degenerations

 HERMANN WEYL LECTURES Topic: The Ax Conjecture and Degenerations Speaker: János Kollár Affiliation: Princeton University Date: Monday, March 12 Time/Room: 3:00pm - 4:00pm/S-101

Lecture 4. The Ax conjecture and degenerations. Originating with his studies on the logic of finite fields, James Ax conjectured that every PAC field is $C_1$. The recent proof of this in characteristic 0 is connected with degenerations of rationally connected varieties. Work of Hacon, Hogadi, K., McKernan and Xu.