János Kollár

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

Kollár studied at the Eötvös University in Budapest and was at Brandeis University in 1984 with a doctorate Teruhisa Matsusaka ( Canonical Threefolds ). After that, he was from 1984 to 1987 Junior Fellow at Harvard University and from 1987 to 1999 professor at the University of Utah before 1999 he became a professor at Princeton University.

Kollár worked on the birational geometry of higher-dimensional algebraic varieties. In particular, he was involved in the 1980s in the program of Shigefumi Mori for the classification of three-dimensional algebraic varieties. He was a pioneer in the theory rationally related varieties ( ie such algebraic varieties, on which enough rational curves are available to connect any 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 of John Nash of 1952. Nash had proved that a compact differentiable manifold is diffeomorphic to the set of zeros of real polynomials. He suspected, conversely, that every such manifold is a differentiable real algebraic variety exists, the birationally equivalent to a projective space and is diffeomorphic to the real points of. While it was known that she was wrong in two dimensions, but in general the accuracy was adopted in higher dimensions, to Kollár in his classification of differentiable structures of 3- varieties, birational were equivalent to the projective space, counter-examples found.

Kollár in 2006 received the Cole prize in algebra. 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 on the second European Congress of Mathematicians in Budapest (Low degree polynomial equations: arithmetic, geometry and topology ). He was selected as Plenarsprecher at the International Congress of Mathematicians 2014 in Seoul.

In 1995 he was elected to the Hungarian Academy of Sciences and in 2005 to the National Academy of Sciences.

Writings

• Shafarevich Maps and Automorphic Forms. Princeton University Press, 1995.
• Rational Curves on Algebraic Varieties. Springer -Verlag 2001, results in mathematics, ISBN 3,540,601,686th
• With Shigefumi Mori: Geometry of Algebraic Varieties birational. Cambridge Tracts in Mathematics, Cambridge University Press, 1998, ISBN 0521632773 ( Iwanami Shoten in Japanese ).
• Lectures on Resolution of Singularities. Princeton University Press, 2007.