James McKernan

James McKernan ( born March 19, 1964 in London ) is a British mathematician who deals with algebraic geometry.

McKernan studied at Cambridge University ( BA 1985) and his Ph.D. in 1991 from Harvard University under Joe Harris ( On the Hyperplane Sections of a Variety in Projective Space). As a post-doc, he was at the University of Utah (1991-1993), at the University of Texas at Austin, at Oklahoma State University in Stillwater (1994 /5). From 1995 he was a professor at the University of California, Santa Barbara, and from 2007 professor at the Massachusetts Institute of Technology.

McKernan managed with Christopher Hacon a breakthrough in the birational classification of higher-dimensional algebraic varieties. For two-dimensional varieties, the classification in the 19th century it was known in the 1980s, this was achieved by Shigefumi Mori and other three-dimensional varieties ( Mori was awarded the Fields Medal ). With the help of flips called birational transformations ( as well as of divisorial contractions ) the varieties are thereby attributed to minimal models. Hacon and McKernan succeeded in proving the existence of flips in any dimension and the proof of the finiteness of the flip- chains in the minimal models of the program. Prior to the work of Hacon and McKernan the case of more than three dimensions was largely open.

In 2007 he was awarded the Clay Research Award. In 2009 he received the Cole prize in algebra with Hacon. In 2010, he was with Hacon Invited Speaker at the International Congress of Mathematicians in Hyderabad ( flips and flops, boundedness results in birational geometry ).

Writings

• With Hacon: boundedness of pluricanonical maps of varieties of general type, Inventiones Mathematicae, Bd.166, 2006, p.1 -25
• With Hacon: Extension theorems and the existence of flips, in A. Corti (Editor) flips for 3folds and 4folds, Oxford Lecture Series in Mathematics and Applications, Bd.37, Oxford University Press 2007, p.76 -110