Andrei Okounkov
Encyclopedia
Andrei Yuryevich Okounkov (born 1969) is a Russia
n mathematician
who works on representation theory
and its applications to algebraic geometry
, mathematical physics
, probability theory
and special functions. He is currently a professor at Columbia University
.
in 1995 under Alexandre Kirillov
. He has been a professor at Columbia University
since 2010. He has previously been a professor at Princeton University
from 2002 to 2010, an assistant and associate professor at the University of California, Berkeley
, and an instructor at the University of Chicago
.
of the Hilbert scheme
of points in the complex plane
. Much of his work on Hilbert schemes was joint with Rahul Pandharipande
.
Okounkov along with Pandharipande, Nikita Nekrasov
, and Davesh Maulik, has formulated well-known conjectures relating the Gromov–Witten invariants and Donaldson–Thomas invariants of threefolds.
Okounkov has an Erdős number
of at most three, via Anatoly Vershik
and Gregory A. Freiman.
In 2006, at the 25th International Congress of Mathematicians
in Madrid
, Spain
he received the Fields Medal
"for his contributions to bridging probability, representation theory and algebraic geometry."
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who works on representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
and its applications to algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
and special functions. He is currently a professor at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
.
Education and career
He received his doctorate at Moscow State UniversityMoscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
in 1995 under Alexandre Kirillov
Alexandre Kirillov
Alexandre Aleksandrovich Kirillov is a Soviet and Russian mathematician, renowned for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory....
. He has been a professor at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
since 2010. He has previously been a professor at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
from 2002 to 2010, an assistant and associate professor at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, and an instructor at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
.
Work
He has worked on the representation theory of infinite symmetric groups, the statistics of plane partitions, and the quantum cohomologyQuantum cohomology
In mathematics, specifically in symplectic topology and algebraic geometry, a quantum cohomology ring is an extension of the ordinary cohomology ring of a closed symplectic manifold. It comes in two versions, called small and big; in general, the latter is more complicated and contains more...
of the Hilbert scheme
Hilbert scheme
In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space , refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials...
of points in the complex plane
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...
. Much of his work on Hilbert schemes was joint with Rahul Pandharipande
Rahul Pandharipande
Rahul Pandharipande is a mathematician at the Swiss Federal Institute of Technology Zurich , working in algebraic geometry, especially Gromov-Witten theory....
.
Okounkov along with Pandharipande, Nikita Nekrasov
Nikita Nekrasov
-Background:Nerkrasov was born in Moscow, Russia and attended the Moscow State 57th School, graduating in 1995. He went on to graduate with honors from Moscow Physical Technical Institute in 1995. Nekrasov did his graduate work at Princeton University, receiving his PhD in 1996...
, and Davesh Maulik, has formulated well-known conjectures relating the Gromov–Witten invariants and Donaldson–Thomas invariants of threefolds.
Okounkov has an Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
of at most three, via Anatoly Vershik
Anatoly Vershik
Anatoly Moiseevich Vershik is a Soviet and Russian mathematician. He is most famous for his joint work with Sergey V. Kerov on representations of infinite symmetric groups and applications to the longest increasing subsequences....
and Gregory A. Freiman.
In 2006, at the 25th International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in Madrid
Madrid
Madrid is the capital and largest city of Spain. The population of the city is roughly 3.3 million and the entire population of the Madrid metropolitan area is calculated to be 6.271 million. It is the third largest city in the European Union, after London and Berlin, and its metropolitan...
, Spain
Spain
Spain , officially the Kingdom of Spain languages]] under the European Charter for Regional or Minority Languages. In each of these, Spain's official name is as follows:;;;;;;), is a country and member state of the European Union located in southwestern Europe on the Iberian Peninsula...
he received the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
"for his contributions to bridging probability, representation theory and algebraic geometry."