Paul Vojta

Paul Vojta 2008

Paul Alan Vojta (born September 30, 1957 ) is an American mathematician who works in the field of number theory and arithmetic algebraic geometry.

life and work

Vojta first studied at the University of Minnesota (Bachelor 1978). He then studied at Harvard University , where he completed his studies with a master's degree in 1980 and a doctorate in 1983 with Barry Mazur . He was then until 1986 Gibbs instructor for mathematics at Yale University . In 1989 he was assistant professor at the University of California, Berkeley and from 1992 a full professor there. In 1996/7 and 1989/90 he was at the Institute for Advanced Study in Princeton, New Jersey .

Vojta attracted attention through his work on number theory and arithmetic geometry. He was able to show analogies between the value distribution theory of Rolf Nevanlinna in function theory (and in the higher-dimensional case generally to hyperbolic geometry) and Diophantine geometry ( theorem of Thue-Siegel-Roth in the form of Freeman Dyson ), which led to a new proof of the Mordell presumption ( Faltings theorem) led (in the function field and number field case).

He was a Putnam Fellow in 1977. In 1992 he received the Cole Prize in number theory. In 1990 he gave an invited lecture at the International Congress of Mathematicians in Kyoto on arithmetic and hyperbolic geometry . In 1975 he won 3rd place with the US team at the Mathematics Olympiad in Bulgaria. He is a fellow of the American Mathematical Society .

As a programmer he is the author of the dvi previewer xdvi (dvi is the format for TeX files).

Fonts

A higher dimensional Mordell conjecture in Cornell, Silverman (Ed.) Arithmetic geometry Springer, 1986, 1998
Diophantine approximations and value distribution theory , Springer Lecturenotes in Mathematics No. 1239, 1987, ISBN 0-387-17551-2
Dyson's Lemma for products of two curves of arbitrary genus , Inv. Math., Vol. 98, 1989, pp. 107-114
Mordells conjecture over function fields , Inventiones Mathematicae Volume 98, 1989, p. 115
Siegel's theorem in the compact case Annals of Math. Vol. 133, 1991, pp. 509-548 (new proof of Faltings' theorem / Mordell's conjecture)
Integral points on subvarieties of semiabelian varieties , Part 1, Inv. Math., Vol. 126, 1996, pp. 133-181
Nevanlinna theory and Diophantine Approximation , in Schneider, Siu (Ed.) Several complex variables , MSRI Publications 1999, online
Recent developments in the relation between diophantine problems and Nevanlinna theory , lecture MSRI 1998
A more general ABC conjecture , Int. Math. Research Notes, Vol. 21, 1998, pp. 1103-1116
On the ABC conjecture and diophantine approximation by rational points , Am. J. Math., Vol. 122, 2000, pp. 843-872, Correction Vol. 123, 2001, pp. 383-384

literature

Serge Lang Hyperbolic and diophantine analysis , Bulletin AMS April 1986
ders. Diophantine problems in complex hyperbolic analysis , in Ribet (Ed.) Current trends in arithmetic algebraic geometry , AMS 1987, online
ders. Vojtas conjectures , in the Bonn work conference 1984, Springer Lecturesnotes in Mathematics Vol. 1111

Web links

personal data
SURNAME	Vojta, Paul
ALTERNATIVE NAMES	Vojta, Paul Alan (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	September 30, 1957