Paul Vojta
Encyclopedia
Paul Alan Vojta is an American
mathematician, known for his work in number theory
on diophantine geometry
and diophantine approximation
.
In formulating a number of striking conjecture
s, he pointed out the possible existence of parallels between the Nevanlinna theory
of complex analysis
, and diophantine analysis. This was a novel contribution to the circle of ideas around the Mordell conjecture and abc conjecture
, suggesting something of large importance to the integer solutions (affine space
) aspect of diophantine equation
s. It has been taken up in his own work, and that of others.
He was an undergraduate student at the University of Minnesota
, where he was a Putnam Fellow, and a doctoral student at Harvard University
(1983). He currently is a professor in the Department of Mathematics at the University of California, Berkeley
.
Vojta has also written the popular .dvi
-previewer xdvi.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician, known for his work in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
on diophantine geometry
Diophantine geometry
In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not algebraically closed, such as the field of rational numbers or a finite field, or more general...
and diophantine approximation
Diophantine approximation
In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers....
.
In formulating a number of striking conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
s, he pointed out the possible existence of parallels between the Nevanlinna theory
Nevanlinna theory
Nevanlinna theory is a branch of complex analysis developed by Rolf Nevanlinna. It deals with the value distribution theory of holomorphic functions in one variable, usually denoted z....
of complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, and diophantine analysis. This was a novel contribution to the circle of ideas around the Mordell conjecture and abc conjecture
Abc conjecture
The abc conjecture is a conjecture in number theory, first proposed by Joseph Oesterlé and David Masser in 1985. The conjecture is stated in terms of three positive integers, a, b and c , which have no common factor and satisfy a + b = c...
, suggesting something of large importance to the integer solutions (affine space
Affine space
In mathematics, an affine space is a geometric structure that generalizes the affine properties of Euclidean space. In an affine space, one can subtract points to get vectors, or add a vector to a point to get another point, but one cannot add points. In particular, there is no distinguished point...
) aspect of diophantine equation
Diophantine equation
In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations...
s. It has been taken up in his own work, and that of others.
He was an undergraduate student at the University of Minnesota
University of Minnesota
The University of Minnesota, Twin Cities is a public research university located in Minneapolis and St. Paul, Minnesota, United States. It is the oldest and largest part of the University of Minnesota system and has the fourth-largest main campus student body in the United States, with 52,557...
, where he was a Putnam Fellow, and a doctoral student at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
(1983). He currently is a professor in the Department of Mathematics at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
.
Vojta has also written the popular .dvi
DVI (file format)
The Device independent file format is the output file format of the TeX typesetting program, designed by David R. Fuchs in 1979. Unlike the TeX markup files used to generate them, DVI files are not intended to be human-readable; they consist of binary data describing the visual layout of a...
-previewer xdvi.