Paul Alan Vojta (born September 30, 1957) is an American mathematician, known for his work in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
on
Diophantine geometry
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 ...
and
Diophantine approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.
The first problem was to know how well a real number can be approximated by r ...
.
Contributions
In formulating
Vojta's conjecture In mathematics, Vojta's conjecture is a conjecture introduced by about heights of points on algebraic varieties over number fields. The conjecture was motivated by an analogy between diophantine approximation and Nevanlinna theory (value distributi ...
, he pointed out the possible existence of parallels between the
Nevanlinna theory In the mathematical field of complex analysis, Nevanlinna theory is part of the
theory of meromorphic functions. It was devised in 1925, by Rolf Nevanlinna. Hermann Weyl called it "one of the few great mathematical events of (the twentieth) century ...
of
complex analysis, and
diophantine analysis
In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...
in the circle of ideas around the
Mordell conjecture
Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction.
Educati ...
and
abc conjecture
The ''abc'' conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. It is stated in terms of three positive integers ''a'', ''b'' ...
. This suggested the importance of the ''integer solutions'' (
affine space
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related ...
) aspect of
diophantine equations.
Vojta wrote the
.dvi-previewer
xdvi
xdvi is an open-source computer program written by Paul Vojta for displaying TeX-produced .dvi files under the X Window System on Unix, including Linux.
The xdvi interface has a set of GUI controls and a window displaying a single page of the ...
.
Education and career
He was an undergraduate student at the
University of Minnesota
The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Tw ...
, where he became a
Putnam Fellow
The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regar ...
in 1977,
and a doctoral student at
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
(1983). He currently is a professor in the Department of Mathematics at the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
.
Awards and honors
In 2012 he became a fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
List of Fellows of the American Mathematical Society
retrieved 2013-08-29.
Selected publications
* ''Diophantine Approximations and Value Distribution Theory'', Lecture Notes in Mathematics 1239, Springer Verlag, 1987,
References
External links
Vojta's home page
*
1957 births
Living people
Arithmetic geometers
Putnam Fellows
Institute for Advanced Study visiting scholars
University of Minnesota alumni
Harvard University alumni
University of California, Berkeley faculty
20th-century American mathematicians
Fellows of the American Mathematical Society
International Mathematical Olympiad participants
21st-century American mathematicians
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