Paul Vojta | |
|---|---|
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| Born | September 30, 1957 |
| Nationality | American |
| Alma mater | Harvard University University of Minnesota |
| Known for | Vojta's conjecture |
| Awards | Cole Prize (1992) Putnam Fellow |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of California, Berkeley |
| Doctoral advisor | Barry Mazur |
Paul Alan Vojta (born September 30, 1957) is an American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation.
In formulating Vojta's conjecture, he pointed out the possible existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis in the circle of ideas around the Mordell conjecture and abc conjecture. This suggested the importance of the integer solutions (affine space) aspect of diophantine equations.[ citation needed ]
He was an undergraduate student at the University of Minnesota, where he became a Putnam Fellow in 1977, [1] and a doctoral student at Harvard University (1983). [2] He currently is a professor in the Department of Mathematics at the University of California, Berkeley.
In 2012 he became a fellow of the American Mathematical Society. [3]
John Edensor Littlewood was a British mathematician. He worked on topics relating to analysis, number theory, and differential equations, and had a lengthy collaboration with G. H. Hardy and Mary Cartwright.
In arithmetic geometry, the Mordell conjecture is the conjecture made by Louis Mordell that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points. In 1983 it was proved by Gerd Faltings, and is now known as Faltings's theorem. The conjecture was later generalized by replacing Q by any number field.
In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations.
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In mathematics, Vojta's conjecture is a conjecture introduced by Paul Vojta (1987) about heights of points on algebraic varieties over number fields. The conjecture was motivated by an analogy between diophantine approximation and Nevanlinna theory in complex analysis. It implies many other conjectures in Diophantine approximation, Diophantine equations, arithmetic geometry, and mathematical logic.
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