János Kollár (born 7 June 1956) is a
Hungarian mathematician, specializing in
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
.
Professional career
Kollár began his studies at the
Eötvös University in Budapest and later received his PhD at
Brandeis University
Brandeis University () is a Private university, private research university in Waltham, Massachusetts, United States. It is located within the Greater Boston area. Founded in 1948 as a nonsectarian, non-sectarian, coeducational university, Bra ...
in 1984 under the direction of
Teruhisa Matsusaka with a thesis on canonical threefolds. He was
Junior Fellow at
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
from 1984 to 1987 and professor at the
University of Utah from 1987 until 1999. Currently, he is professor at
Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
.
Contributions
Kollár is known for his contributions to the
minimal model program for
threefolds and hence the
compactification of
moduli of
algebraic surfaces, for pioneering the notion of
rational connectedness (''i.e.'' extending the theory of
rationally connected varieties for varieties over the complex field to varieties over
local fields), and finding
counterexamples to a conjecture of
John Nash. (In 1952 Nash conjectured a converse to a famous theorem he proved, and Kollár was able to provide many 3-dimensional counterexamples from an important new structure theory for a class of 3-dimensional algebraic varieties.)
Kollár also gave the first algebraic proof of
effective Nullstellensatz: let
be polynomials of degree at most
in
variables; if they have no common zero, then the equation
has a solution such that each polynomial
has degree at most
.
Awards and honors
Kollár is a member of the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
since 2005 and received the
Cole Prize in 2006. He is an external member of the
Hungarian Academy of Sciences since 1995. 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, ...
. In 2016 he became a fellow of the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
. In 2017 he received the
Shaw Prize in Mathematical Sciences.
In 1990 he was an
invited speaker at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before ...
(ICM) in
Kyōto. In 1996 he gave one of the plenary addresses at the
European Mathematical Congress in
Budapest
Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...
(''Low degree polynomial equations: arithmetic, geometry and topology''). He was also selected as a plenary speaker at the ICM held in 2014 in
Seoul
Seoul, officially Seoul Special Metropolitan City, is the capital city, capital and largest city of South Korea. The broader Seoul Metropolitan Area, encompassing Seoul, Gyeonggi Province and Incheon, emerged as the world's List of cities b ...
.
As a high school student, Kollár represented Hungary and won Gold medals at both the 1973 and 1974
International Mathematical Olympiads.
Works
*
*
* (Japanese by Iwanami Shoten).
*
*
References
External links
*
Homepage in Princeton
{{DEFAULTSORT:Kollar, Janos
1956 births
Living people
Algebraic geometers
20th-century American mathematicians
20th-century Hungarian mathematicians
21st-century American mathematicians
21st-century Hungarian mathematicians
Institute for Advanced Study visiting scholars
Harvard Fellows
University of Utah faculty
Princeton University faculty
Brandeis University alumni
Eötvös Loránd University alumni
Members of the Hungarian Academy of Sciences
Members of the United States National Academy of Sciences
Fellows of the American Mathematical Society
International Mathematical Olympiad participants
Fellows of the American Academy of Arts and Sciences