János Kollár (born 7 June 1956) is a
Hungarian mathematician, specializing in
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
.
Professional career
Kollár began his studies at the
Eötvös University in Budapest and later received his PhD at
Brandeis University
, mottoeng = "Truth even unto its innermost parts"
, established =
, type = Private research university
, accreditation = NECHE
, president = Ronald D. Liebowitz
, ...
in 1984 under the direction of
Teruhisa Matsusaka
(1926–2006) was a Japanese-born American mathematician, who specialized in algebraic geometry.
Matsusaka received his Ph.D. in 1952 at Kyoto University; he was a member of the Brandeis Mathematics Department from 1961 until his retirement in 1 ...
with a thesis on canonical threefolds. He was
Junior Fellow
The Society of Fellows is a group of scholars selected at the beginnings of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intell ...
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 ...
from 1984 to 1987 and professor at the
University of Utah
The University of Utah (U of U, UofU, or simply The U) is a public research university in Salt Lake City, Utah. It is the flagship institution of the Utah System of Higher Education. The university was established in 1850 as the University of De ...
from 1987 until 1999. Currently, he is professor at
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
.
Contributions
Kollár is known for his contributions to the
minimal model program
In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its or ...
for
threefolds and hence the
compactification
Compactification may refer to:
* Compactification (mathematics), making a topological space compact
* Compactification (physics), the "curling up" of extra dimensions in string theory
See also
* Compaction (disambiguation)
Compaction may refer t ...
of
moduli of
algebraic surfaces, for pioneering the notion of
rational
Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abi ...
connectedness
In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected. When a disconnected object can be s ...
(''i.e.'' extending the theory of
rationally connected varieties for varieties over the complex field to varieties over
local field
In mathematics, a field ''K'' is called a (non-Archimedean) local field if it is complete with respect to a topology induced by a discrete valuation ''v'' and if its residue field ''k'' is finite. Equivalently, a local field is a locally compact ...
s), and finding
counterexamples
A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "John Smith is not a lazy student" is ...
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, 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 Nati ...
since 2005 and received the
Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...
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 (abbreviation: AAA&S) 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 ...
. 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 Nevanlinna Prize (to be rename ...
(ICM) in
Kyōto
Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the c ...
. In 1996 he gave one of the plenary addresses at the
European Mathematical Congress
The European Congress of Mathematics (ECM) is the second largest international conference of the mathematics community, after the International Congresses of Mathematicians (ICM).
The ECM are held every four years and are timed precisely between ...
in
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...
(''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 known as the Seoul Special City, is the capital and largest metropolis of South Korea.Before 1972, Seoul was the ''de jure'' capital of the Democratic People's Republic of Korea (North Korea) as stated iArticle 103 ...
.
As a high school student, Kollár represented Hungary and won Gold medals at both the 1973 and 1974
International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...
s.
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