Abstract: Algebraic geometry is the study of geometric objects (varieties) defined by polynomial equations. In recent years that has been much progress towards understanding the geometry of complex projective varieties in all dimensions. The main approach is the so called minimal model program or MMP initiated by S. Mori in the 80's.
In contrast algebraic geometry over an algebraically closed field of positive characteristic (or in mixed characteristics) is much less understood.
In this talk I will discuss recent progress in dimension 3, 4 towards establishing the MMP in positive and mixed characteristics.

Speaker: Christopher Hacon is a world renowned mathematician working in algebraic geometry. He has made many fundamental contributions in the field of birational geomety. He has been honored with prestigious awards such as the 2018 Breakthrough Prize in Mathematics, the 2016 EH Moore Research Article Prize, the 2011 Antonio Feltrinelli Prize in Mathematics Mechanics and Applications, the 2009 Frank Nelson Cole Prize in Algebra and the 2007 Clay Research Award. He is a member of the American Academy of Arts and Sciences, a fellow of the American Mathematical Society, a member of the National Academy of Sciences, and a fellow of the Royal Society of London.