A Fields medallist Andrei Okounkov, will deliver a public lecture at the 8th European Congress of Mathematics.

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.

(Photo: Higher School of Economics, National Research University)

A Fields medallist Sir Vaughan F. R. Jones, will deliver a public lecture at the 8th European Congress of Mathematics.

Sir Vaughan F. R. Jones is a New Zealand-born mathematician based in the USA, renowned worldwide for his remarkable work on von Neumann algebras and knot polynomials.

He was awarded a Fields medal in 1990 for his discoveries in the mathematical study of knots – including an improvement on the Alexander polynomial (now called the Jones polynomial) – working from an unexpected direction with origins in the theory of von Neumann algebras, an area of analysis already much developed by Alain Connes. These discoveries led to the solution of a number of classical problems in knot theory, and to increased interest in low-dimensional topology.

His work on polynomial invariants of knots also had remarkable implications in the field of molecular biology, where new insight was gained into how DNA can remove the tangles that result when replication and cell division firstly duplicates the DNA and subsequently has to pull the chromosomal mass into different cells. The result represents a landmark in modern mathematics whose ramifications still remain to be fully explored.

Prof. Jones is currently Professor Emeritus at University of California, Berkeley, where he has been on the faculty since 1985, as well as Stevenson Distinguished Professor of Mathematics at Vanderbilt University (from 2011). He is also a Distinguished Alumni Professor at the University of Auckland.