Mathematics Department Colloquium/Bowen Lectures: Lecture 3: Birational geometry in characteristic $p >0$

Colloquium | February 21 | 4:10-5 p.m. | 60 Evans Hall

 Christopher Hacon, University of Utah

 Department of Mathematics

After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (e.g. the solution set of a system of polynomial equations defined by $p_1,...,p_r$ in $C[x_1,...,x_n]$) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic $p >0$. Many technical difficulties arise in this context. Nevertheless, there has been much progress recently. In particular, the MMP was established for 3-folds in characteristic $p >5$ by work of Birkar, Hacon, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.