Christopher Hacon

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Hacon in Oberwolfach 2008

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

Life

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

plant

With James McKernan, Hacon achieved a breakthrough in the birational classification of higher-dimensional algebraic varieties . The classification of two-dimensional varieties was already known in the 19th century; Shigefumi Mori and others succeeded in doing this in the 1980s for three-dimensional varieties (Mori received the Fields Medal for this ). With the help of birational transformations called flips (as well as divisorial contractions ), the varieties are reduced to minimal models : Fano varieties (positive curvature), Calabi-Yau varieties (zero curvature) and varieties of general type (negative curvature). Hacon and McKernan succeeded in proving the existence of flips in any dimension and proving the finiteness of the flip chains in the program of minimal models, that is, they proved that such a reduction to minimal models in a finite number of steps is always possible. Before the work of Hacon and McKernan, the case of more than three dimensions was largely open ( Vyacheslav Vladimirovich Shokurov showed the existence of flips in four dimensions in 2003). A joint work by Caucher Birkar , Paolo Cascini , McKernan and Hacon (BCHM) from 2006 (published 2010) was of crucial importance .

Awards

In 2003 he was a Sloan Research Fellow . In 2007 he received the Clay Research Award with McKernan and in 2009 both received the Cole Award in Algebra. In 2010 he was invited speaker with McKernan at the International Congress of Mathematicians in Hyderabad ( Boundedness results in birational geometry , flips and flops ). 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 , of the American Academy of Arts and Sciences since 2017 and of the National Academy of Sciences since 2018 . In 2018 he received the Breakthrough Prize in Mathematics and has been a member of the Royal Society since 2019 .

Fonts

  • with McKernan: Boundedness of pluricanonical maps of varieties of general type. In: Inventiones Mathematicae , Volume 166, 2006, pp. 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, Volume 37), Oxford University Press, 2007, pp. 76-110.
  • with Caucher Birkar , Cascini, McKernan: Existence of minimal models for varieties of log general type I. In: Journal of the American Mathematical Society. Volume 23, 2010, pp. 405–468, arxiv : math / 0610203 (Preprint 2006), Part 2 with McKernan, ibid., Pp. 469–490, arxiv : 0808.1929 (Preprint 2008)
  • Higher dimensional minimal program for varieties of general type. Park City Mathematics Institute (PCMI) Lectures, 2008

Web links

Commons : Christopher Hacon  - Collection of images, videos and audio files

Individual evidence

  1. ↑ Recognition of the Fields Medal for Birkar 2018 by Allyn Jackson, official website of the IMU for the Fields Medal 2018
personal data
SURNAME Hacon, Christopher
ALTERNATIVE NAMES Hacon, Christopher Derek (full name); Hacon, Christopher D.
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH February 14, 1970
PLACE OF BIRTH Manchester