Andrei Yuryevich Okounkov (russian: Андре́й Ю́рьевич Окунько́в, ''Andrej Okun'kov'') (born July 26, 1969) is a Russian mathematician who works on representation theory and its applications to

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 ...

, mathematical physics, probability theory and special functions. He is currently a professor at the University of California, Berkeley and the academic supervisor of HSE International Laboratory of Representation Theory and Mathematical Physics. In 2006, he received the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

"for his contributions to bridging probability, representation theory and algebraic geometry.""Information about Andrei Okounkov, Fields Medal winner"
ICM Press Release

Education and career

He received his doctorate at Moscow State University in 1995 under

Alexandre Kirillov Alexandre Aleksandrovich Kirillov (russian: Алекса́ндр Алекса́ндрович Кири́ллов, born 1936) is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups a ...

and Grigori Olshanski. He was a professor at Columbia University between 2010 and 2022. He was previously 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. He rejoined the faculty at Berkeley in the summer of 2022.

Work

He has worked on the representation theory of

infinite symmetric group In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group \m ...

s, the statistics of

plane partition In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers \pi_ (with positive number, positive integer indices ''i'' and ''j'') that is nonincreasing in both indices. This means that : \pi ...

s, and the

quantum 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, t ...

of the

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 (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a d ...

of points in the

complex plane In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the -axis, called the real axis, is formed by the real numbers, and the -axis, called the imaginary axis, is formed by the ...

. Much of his work on Hilbert schemes was joint with

Rahul Pandharipande Rahul Pandharipande (born 1969) is a mathematician who is currently a professor of mathematics at the Swiss Federal Institute of Technology Zürich (ETH) working in algebraic geometry. His particular interests concern moduli spaces, enumerativ ...

. Okounkov, along with Pandharipande, Nikita Nekrasov, and Davesh Maulik, has formulated well-known conjectures relating the

Gromov–Witten invariant In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic man ...

s and Donaldson–Thomas invariants of threefolds. In 2006, at the 25th

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 ...

in Madrid, Spain, he received the

"for his contributions to bridging probability, representation theory and algebraic geometry." In 2016 he became a fellow of the American Academy of Arts and Sciences.

Education and career

Work

See also

References

External links