# Andrei Yuryevich Okounkov

### Quick Info

Moscow, Russia

**Andrei Yuryevich Okounkov**won a Fields Medal in 2006 for his contributions bridging probability, representation theory and algebraic geometry.

### Biography

**Andrei Yuryevich Okounkov**was educated in Moscow where he attended Moscow State University. However, his route was not quite the rapid one taken by many who go on to acquire the highest achievements [7]:-

I didn't go through special schools and olympiads. I came via studying economics and army service. I had a family before papers. As a result, my mind is probably not as quick as it could have been with an early drilling in math. But perhaps I also had some advantages over my younger classmates. I had a broader view of the universe and a better idea about the place of mathematics in it. This helped me form my own opinion about what is important, beautiful, promising, etc.After the award of his first degree, Okounkov remained at Moscow State University undertaking research for his Candidate's degree (equivalent to a Ph.D.) supervised by Alexander Aleksandrovich Kirillov. He explained in [7] the importance of his teachers at this time in his mathematical development:-

Growing up in Kirillov's seminar, I had in its participants, especially in Grisha Ol'shanskii, wonderful teachers who generously invested their time and talent into explaining mathematics and who patiently followed my first professional steps. I can't imagine becoming a mathematician without them. So it must be that in this respect my professional formation resembles everybody else's.Okounkov was awarded his Candidate's degree in 1995 for his thesis

*Admissible Representation of Gelfand Pairs Associated with the Infinite Symmetric Group*. Before the award of this degree, he already had papers in print such as

*Thoma's theorem and representations of an infinite bisymmetric group*(Russian) (1994) and

*On the representation of orbits in the form of the sum of elementary orbits*(Russian) (1994). He was appointed as a research fellow in the Dobrushin Mathematical Laboratory at the Institute for Problems of Information Transmission at the Russian Academy of Sciences. Moving to the United States, he spent time at the Mathematical Science Research Institute in Berkeley in the academic year 1996-97 financially supported by a grant from the National Science Foundation. While there he wrote the paper

*Proof of a Conjecture of Goulden and Jackson*. His abstract reads:-

We prove an integration formula involving Jack polynomials conjectured by I P Goulden and D M Jackson in connection with enumeration of maps in surfaces.In 1997 he was appointed an Instructor at the University of Chicago, a position he held for three years. He also spent some time at the Institute for Advanced Study at Princeton. Appointed as an Assistant Professor at the University of California at Berkeley, he held a Alfred P Sloan Research Fellowship in 2000 and a Fellowship from the David and Lucile Packard Foundation in 2001. Packard Fellowships are awarded to researchers in mathematics, natural sciences, computer science, and engineering who are in the first three years of a faculty appointment.

In 2002 Okounkov was appointed as a Professor at Princeton University. He received a European Mathematical Society Prize 2004. The citation reads:-

Andrei Okounkov ... contributed greatly to the field of asymptotic combinatorics. An extremely versatile mathematician, he found a wide array of applications of his methods. His early results include a proof of a conjecture of Ol'shanskii on the representations theory of groups with infinite-dimensional duals. Okounkov gave the first proof of the celebrated Baik-Deift-Johansson conjecture, which states that the asymptotics of random partitions distributed according to the Plancherel measure coincides with that of the eigenvalues of large Hermitian matrices. An important and influential result of Okounkov is a formula he found in joint work with Borodin, which expresses a general Toeplitz determinant as the Fredholm determinant of the product of two associated Hankel operators. The new techniques of working with random partitions invented and successfully developed by Okounkov lead to a striking array of applications in a wide variety of fields: topology of module spaces, ergodic theory, the theory of random surfaces and algebraic geometry.His greatest honour has been the award of a Fields medal at The International Congress of Mathematicians held at Madrid in August 2006:-

For his contributions bridging probability, representation theory and algebraic geometry.The press release concerning his award begins:-

The work of Andrei Okounkov has revealed profound new connections between different areas of mathematics and has brought new insights into problems arising in physics. Although his work is difficult to classify because it touches on such a variety of areas, two clear themes are the use of notions of randomness and of classical ideas from representation theory. This combination has proven powerful in attacking problems from algebraic geometry and statistical mechanics.Asked about how he felt being awarded a Fields Medal he replied:-

Out of a whole spectrum of thoughts that I had in the time since receiving the phone call from the President of the International Mathematical Union, two are especially recurrent. First, this is a great honour and it means a great responsibility. At times, I feel overwhelmed by both. Second, I can't wait to share this recognition with my friends and collaborators. Mathematics is both a personal and collective endeavour: while ideas are born in individual heads, the exchange of ideas is just as important for progress. I was very fortunate to work with many brilliant mathematician who also became my close personal friends. This is our joint success.He explained in [7] how he went about tackling difficult problems:-

I personally don't know how one can understand something without both thinking about it quietly over and over and discussing it with friends. When I feel puzzled, I like long walks or bike rides. I like to be alone with my computer playing with formulas or experimenting with code. But when I finally have an idea, I can't wait to share it with others. I am so fortunate to be able to share my work and my excitement about it with many brilliant people who are at the same time wonderful friends.Andrew Wiles is quoted in [3] giving this appreciation of his colleague Andrei Okounkov:-

One of his greatest strengths is his amazing versatility. He works in many different fields of mathematics and succeeds in taking results from one area and applying them in a seemingly quite different field.Okounkov left Princeton in 2010 to take up a professorship of mathematics at Columbia University in New York.

### References (show)

- M Cook,
*Mathematicians: An outer view of an inner world*(Princeton University Press, Princeton, 2009). - 2006 Fields Medals awarded,
*Notices Amer. Math. Soc.***53**(9) (2006), 1037-1044. - A Cai, Two Princetonians among four awarded Fields Medal: Okounkov, Tao GS '96 receive award considered Nobel Prize of mathematics,
*The Daily Princetonian*(19 May 2006). - G Felder, The work of Andrei Okounkov,
*International Congress of Mathematicians***I**(European Mathematical Society, Zürich, 2007), 55-64. - R Kenyon, Les travaux d'Andrei Okounkov sur le modèle des diméres,
*Gaz. Math. No.***112**(2007), 18-22. - I Mundet i Riera, 2006 Fields Medal: Andrei Okounkov (Catalan),
*SCM Not. No.***23**(2007), 47-49. - V Munoz and U Persson, Interviews with three Fields medalists,
*Notices Amer. Math. Soc.***54**(3) (2007), 405-410. - A Okounkov, Interview with Andrei Okounkov, Fields Medal, 2006 ICM (Spanish),
*Gac. R. Soc. Mat. Esp.***9**(3) (2006), 655-659. - A M Vershik, J Bourgain, H Kesten and N Reshetikhin, The mathematical work of the 2006 Fields medalists,
*Notices Amer. Math. Soc.***54**(3) (2007), 388-404.

### Additional Resources (show)

Other websites about Andrei Yuryevich Okounkov:

### Honours (show)

Honours awarded to Andrei Yuryevich Okounkov

Written by J J O'Connor and E F Robertson

Last Update March 2011

Last Update March 2011