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 ...

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

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 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 ...

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 ...

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