Paul Vojta

Paul 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 studied at the University of Minnesota (Bachelor, 1978). He then studied at Harvard University, where he graduated with a Master 's degree in 1980 and his doctorate in 1983 at Barry Mazur. He was then to 1986 Gibbs Instructor of Mathematics at Yale University. In 1989 he was assistant professor at the University of California, Berkeley, and from 1992 full professor there. 1996/7 and 1989/90 he was in Princeton, New Jersey at the Institute for Advanced Study.

Vojta excited for his work on number theory and arithmetic geometry attention. He was able to show and diophantine geometry ( set of Thue -Siegel - Roth in the form of Freeman Dyson ) analogies between the value distribution theory of Rolf Nevanlinna in the theory of functions ( generally for hyperbolic geometry and in the higher dimensional case ) that lead to a new proof of Mordellvermutung ( Faltings theorem) led ( in the function body and the number field case).

He was Putnam Fellow 1977. 1992 he received the Cole prize in number theory. In 1990 he held a Invited Lecture at the International Congress of Mathematicians in Kyoto on Arithmetic and hyperbolic geometry. In 1975, he won with the U.S. team to 3rd place in the Mathematics Olympiad in Bulgaria. He is a Fellow of the American Mathematical Society.

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

Writings

  • Vojta Siegel theorem in the compact case Annals of Math Bd.133, 1991, S.509 -548 ( new proof of the theorem of Faltings / conjecture of Mordell )
  • Vojta conjecture over function fields Mordells, Inventiones Mathematicae Bd.98, 1989, p.115
  • Vojta Dyson's lemma for products of two curves of arbitrary genus, Inv.Math.1989
  • Vojta Diophantine approximations and value distribution theory, Springer Lecture Notes in Mathematics Nr.1239, 1987, ISBN 0-387-17551-2
  • Vojta A higher dimensional Mordell conjecture in Cornell, Silverman (eds.) Arithmetic Geometry Springer, 1986, 1998
  • Vojta Nevanlinna theory and Diophantine approximation, in Schneider, Siu (ed.) Several complex variables, MSRI Publications 1999, online here:
  • Vojta, lecture MSRI Recent developments in the relation in between diophantine problems and Nevanlinna theory in 1998
  • Vojta A more general conjecture ABC 1998
  • Vojta On the ABC conjecture and diophantine approximation by rational points in 1999
Princeton (New Jersey) Thue–Siegel–Roth theorem Gerd Faltings Serge Lang Integrated Authority File
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