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 , p ...

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 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 highe ...

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 research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

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 ori ...

for threefolds and hence the compactification of moduli of

algebraic surface In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of di ...

s, 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 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" i ...

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

f_1,\ldots,f_m

be polynomials of degree at most

d \ge 3

n\ge 2

variables; if they have no common zero, then the equation

g_1 f_1+\cdots +g_m f_m=1

has a solution such that each polynomial

g_j

has degree at most

d^n - d

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 Nat ...

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 numbe ...

in 2006. He is an external member of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma ...

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, meeting ...

. 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, a ...

. In 2017 he received the

Shaw Prize The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...

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 rena ...

(ICM) in Kyōto. In 1996 he gave one of the plenary addresses at the European Mathematical Congress 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 o ...

(''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 city, capital and largest metropolis of South Korea.Before 1972, Seoul was the ''de jure'' capital of the North Korea, Democratic People's Republic of Korea (North Korea ...

. 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, excep ...

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