Andrei Okounkov is a Russian mathematician who works in mathematical physics and neighboring areas of representation theory and algebraic geometry.
Enumerative geometry lies at the crossroads of all these fields of mathematics, and a lot of Okounkov's recent work focuses on K-theoretic generalizations of classical questions in enumerative geometry. In particular, a K-theoretic generalization of the Donaldson-Thomas-style counting of curves in algebraic threefolds is an exciting area at the forefront of current research with a conjectural relation to counting membranes of M-theory put forward by Nekrasov and Okounkov, and a geometric representation theory description of it basic building blocks obtained by Okounkov and A.Smirnov. Earlier conjectures of Maulik-Nekrasov-Okounkov-Pandharipande connecting cohomological DT counts with Gromov-Witten theory of algebraic threefolds in many ways shaped the developments of both fields. The proof of the MNOP conjectures for toric varieties by Maulik-Oblomkov-Okounkov-Pandharipande, and the work that followed, extends, among other things, the representation-theoretic understanding of the Gromov-Witten theory of curves (and also of the point) obtained in the early 2000s by Okounkov and Pandharipande.
In 2004, Okounkov was awarded an EMS prize for work that “contributed greatly to the field of asymptotic combinatorics.” 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."
Andrei Okounkov is a professor at the Columbia University in the city of New York and at the Skolkovo Institute of Science and Technology in Moscow, he also serves as the academic supervisor of HSE International Laboratory of Representation Theory and Mathematical Physics. His previous positions include the University of Chicago, University of California at Berkeley, and Princeton University.
We look forward to welcoming Professor Okounkov at the 8th European Congress of Mathematics in Portorož, Slovenia!
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(Photo: Higher School of Economics, National Research University)