János Kollár

János Kollár (born June 7, 1956 in Budapest ) is a Hungarian mathematician who deals with algebraic geometry .

Kollár initially studied at the Eötvös University in Budapest and received his doctorate ( Canonical Threefolds ) at Brandeis University in 1984 with Teruhisa Matsusaka . He was then a Junior Fellow at Harvard University from 1984 to 1987 and a professor at the University of Utah from 1987 to 1999 , before becoming a professor at Princeton University in 1999 . In 1989 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ).

Kollár worked on the birational geometry of higher dimensional algebraic varieties. In particular, he was involved in Shigefumi Mori's program for the classification of three-dimensional algebraic varieties in the 1980s . He was a pioneer in the theory of rationally connected varieties (that is, those algebraic varieties on which there are enough rational curves to connect two points), which he expanded from varieties over the complex numbers to those over local fields.

Kollár also found higher-dimensional counterexamples to a conjecture by John Nash from 1952. Nash had proven that a compact differentiable manifold is diffeomorphic to the zero set of real polynomials. Conversely, he assumed that for every such manifold there exists a differentiable real algebraic variety which is birationally equivalent to the projective space and which is diffeomorphic to the real points of . Although it was known that it was wrong in two dimensions, it was generally assumed that it was correct in higher dimensions, until Kollár found counterexamples in his classification of the differentiable structures of 3 varieties, which were birationally equivalent to projective space. ${\displaystyle M}$ ${\displaystyle M}$ ${\displaystyle M}$

In 1988 he proved an effective version of Hilbert's zero theorem for bodies of any characteristic, after W. Dale Brownawell had given a proof of characteristic zero a year earlier.

Kollár received the Cole Prize in Algebra in 2006 and the Nemmers Prize for Mathematics in 2016 . In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto ( flip and flop ). In 1996 he gave one of the plenary lectures at the second European Congress of Mathematicians in Budapest ( Low degree polynomial equations: arithmetic, geometry and topology ). He was selected as plenary speaker at the International Congress of Mathematicians 2014 in Seoul (The structure of algebraic varieties). For 2017 he was awarded the Shaw Prize in Mathematics.

In 1995 he was elected to the Hungarian Academy of Sciences , 2005 to the National Academy of Sciences and 2016 to the American Academy of Arts and Sciences . He is a fellow of the American Mathematical Society .

Fonts

• Shafarevich Maps and Automorphic Forms. Princeton University Press, 1995.
• Rational Curves on Algebraic Varieties. Springer-Verlag 2001, Results of Mathematics, ISBN 3-540-60168-6 .
• with Shigefumi Mori: Birational Geometry of Algebraic Varieties. Cambridge Tracts in Mathematics, Cambridge University Press, 1998, ISBN 0-521-63277-3 (Japanese by Iwanami Shoten).
• Lectures on Resolution of Singularities. Princeton University Press 2007.

Web links

• Literature by and about János Kollár in the catalog of the German National Library
• Homepage in Princeton
• Notices AMS for the award of the Cole Prize 2006, PDF file (67 kB)

Individual evidence

1. ↑ János Kollár in the Mathematics Genealogy Project (English)
2. ^ American Academy of Arts and Sciences : Newly Elected Fellows. In: amacad.org. Retrieved April 22, 2016 .