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 ]
Vojta wrote the .dvi-previewer xdvi. He also wrote a vi clone. [1]
He was an undergraduate student at the University of Minnesota, where he became a Putnam Fellow in 1977, [2] and a doctoral student at Harvard University (1983). [3] 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. [4]
John Edensor Littlewood was a British mathematician. He worked on topics relating to analysis, number theory, and differential equations and had lengthy collaborations with G. H. Hardy, Srinivasa Ramanujan and Mary Cartwright.
Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field of rational numbers has only finitely many rational points. This was conjectured in 1922 by Louis Mordell, and known as the Mordell conjecture until its 1983 proof by Gerd Faltings. The conjecture was later generalized by replacing 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. Diophantine geometry is part of the broader field of arithmetic geometry.
Klaus Friedrich Roth was a German-born British mathematician who won the Fields Medal for proving Roth's theorem on the Diophantine approximation of algebraic numbers. He was also a winner of the De Morgan Medal and the Sylvester Medal, and a Fellow of the Royal Society.
In mathematics, Roth's theorem or Thue–Siegel–Roth theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have many rational number approximations that are 'very good'. Over half a century, the meaning of very good here was refined by a number of mathematicians, starting with Joseph Liouville in 1844 and continuing with work of Axel Thue, Carl Ludwig Siegel, Freeman Dyson, and Klaus Roth.
Martin David Davis was an American mathematician and computer scientist who contributed to the fields of computability theory and mathematical logic. His work on Hilbert's tenth problem led to the MRDP theorem. He also advanced the Post–Turing model and co-developed the Davis–Putnam–Logemann–Loveland (DPLL) algorithm, which is foundational for Boolean satisfiability solvers.
John William Scott "Ian" Cassels, FRS was a British mathematician.
David William Masser is Professor Emeritus in the Department of Mathematics and Computer Science at the University of Basel. He is known for his work in transcendental number theory, Diophantine approximation, and Diophantine geometry. With Joseph Oesterlé in 1985, Masser formulated the abc conjecture, which has been called "the most important unsolved problem in Diophantine analysis".
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.
A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties to the real numbers.
Peter Clive Sarnak is a South African-born mathematician with dual South-African and American nationalities. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced Study since 2007. He is also Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Sir Andrew Wiles, and is an editor of the Annals of Mathematics. He is known for his work in analytic number theory. He was member of the Board of Adjudicators and for one period chairman of the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.
Wolfgang M. Schmidt is an Austrian mathematician working in the area of number theory. He studied mathematics at the University of Vienna, where he received his PhD, which was supervised by Edmund Hlawka, in 1955. Wolfgang Schmidt is a Professor Emeritus from the University of Colorado at Boulder and a member of the Austrian Academy of Sciences and the Polish Academy of Sciences.
Donald Joseph Newman was an American mathematician. He gave simple proofs of the prime number theorem and the Hardy–Ramanujan partition formula. He excelled on multiple occasions at the annual Putnam competition while studying at City College of New York and New York University, and later received his PhD from Harvard University in 1953.
Richard James Duffin was an American physicist, known for his contributions to electrical transmission theory and to the development of geometric programming and other areas within operations research.
Alan Baker was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.
In mathematics, Vojta's conjecture is a conjecture introduced by Paul Vojta 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.
David William Boyd is a Canadian mathematician who does research on harmonic and classical analysis, inequalities related to geometry, number theory, and polynomial factorization, sphere packing, number theory involving Diophantine approximation and Mahler's measure, and computer computations.
Anatoly Borisovich Katok was an American mathematician with Russian-Jewish origins. Katok was the director of the Center for Dynamics and Geometry at the Pennsylvania State University. His field of research was the theory of dynamical systems.
Manfred Leopold Einsiedler is an Austrian mathematician who studies ergodic theory. He was born in Scheibbs, Austria in 1973.
Vladimir Gennadievich Sprindzuk was a Soviet-Belarusian number theorist.
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