Christopher Hacon

Christopher Derek Hacon ( born February 14, 1970 in Manchester ) is a British mathematician who deals with algebraic geometry.

Hacon studied at the University of Pisa and the Scuola Normale Superiore di Pisa ( bachelor's degree in 1992 ), made in 1995 his Master 's degree at the University of California, Los Angeles ( UCLA), where he received his doctorate in 1998 at Robert Lazarsfeld (* 1953). As a post-doc, he was at the University of Utah and after two years from 2000 as an Assistant Professor at the University of California, Riverside, from 2002 Professor ( first assistant professor from 2005 Associate Professor, from 2008 professor ) at the University of Utah.

Hacon succeeded with James McKernan 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 Shigefumi Mori and others succeeded in 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, that is, they proved that such a reduction to minimal models in finite number of steps is always possible. Prior to the work of Hacon and McKernan the case of more than three dimensions was largely open.

In 2003 he was Sloan Fellow. In 2007 he was awarded the Clay Research Award with McKernan and 2009 both received the Cole prize in algebra. In 2010, he was (geometry boundedness results in birational, flips and flops) with McKernan Invited Speaker at the International Congress of Mathematicians in Hyderabad. In 2011 he was awarded the Antonio Feltrinelli Prize -. In 2012 he gave a plenary lecture at the European Congress of Mathematicians (ECM ) in Krakow ( Classification of algebraic varieties ). He is a Fellow of the American Mathematical Society.

Writings

  • With McKernan: boundedness of pluricanonical maps of varieties of general type, Inventiones Mathematicae, Bd.166, 2006, p.1 -25
  • With McKernan: 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
  • With Birkar, Cascini, McKernan: Existence of minimal models for varieties of log general type I, Preprint 2006, Part II with McKernan, Preprint 2008
  • Higher dimensional minimal program for varieties of general type, Park City Mathematics Institute ( PCMI ) Lectures, 2008
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