UW-PIMS Mathematics Colloquium: Christopher Hacon

Algebraic geometry is the study of geometric objects defined as the solution set of a system of polynomial equations p1,…,pr∈F[x1,…,xn] where F is an algebraically closed field.  After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (eg. F=C) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic p>0.  Despite numerous technical difficulties there has been some interesting recent progress in this direction.  In particular the MMP was established for 3-folds in characteristic p>3 by work of Birkar, Hacon, Witaszek, Xu and others.  In this talk, we will explain some of the challenges and the recent progress in this active area of research.