James McKernan
James McKernan (born March 19, 1964 in London ) is a British mathematician who deals with algebraic geometry.
Life
McKernan graduated from Cambridge University (1985) and received his PhD from Harvard University in 1991 with 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 (1994/95). From 1995 he was professor at the University of California, Santa Barbara and from 2007 professor at the Massachusetts Institute of Technology .
With Christopher Hacon, McKernan achieved a breakthrough in the birational classification of higher-dimensional algebraic varieties. In the case of two-dimensional varieties, the classification was already known in the 19th century by the Italian school . In the 1980s, Shigefumi Mori and others succeeded in classifying three-dimensional varieties (Mori received the Fields Medal for this in 1990). 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. Before the work of Hacon and McKernan, the case of more than three dimensions was largely open (except for four dimensions by Shokurow ). A joint work by Caucher Birkar , Paolo Cascini , McKernan and Hacon (BCHM) from 2006 (published 2010) was of crucial importance .
In 2007 he received the Clay Research Award. In 2009 he received the Cole Prize in Algebra with Hacon. In 2010 he was invited speaker with Hacon at the International Congress of Mathematicians in Hyderabad ( Flips and Flops , Boundedness results in birational geometry ). In 2018 he received the Breakthrough Prize in Mathematics .
Fonts
- with Hacon: Boundedness of pluricanonical maps of varieties of general type . In: Inventiones Mathematicae , Volume 166, 2006, pp. 1-25
- with Caucher Birkar , Cascini, Hacon: 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 Hacon, ibid. Pp. 469-490, arxiv : 0808.1929 Part II Preprint 2008
- with Hacon: Extension theorems and the existence of flips . In: A. Corti (Ed.): Flips for 3folds and 4folds . In: Oxford Lecture Series in Mathematics and Applications , Volume 37, Oxford University Press 2007, pp. 76-110
Web links
Individual evidence
- ↑ Recognition of the Fields Medal for Birkar 2018 by Allyn Jackson, official website of the IMU for the Fields Medal 2018
| personal data | |
|---|---|
| SURNAME | McKernan, James |
| BRIEF DESCRIPTION | British mathematician |
| DATE OF BIRTH | March 19, 1964 |
| PLACE OF BIRTH | London |