Many things around us, such as the distribution of air molecules inside a room, are determined by a law of large numbers: the uniform distribution of molecules is by far the likeliest and it is the one that will occur. I will discuss some examples in which the outcome dictated by the law of large numbers is much more interesting than such uniform spreading and, instead, a beautiful geometry is produced.

Professor Andrei Okounkov was born in Moscow. He is a professor of mathematics at Princeton University. He has also held positions at the Russian Academy of Sciences, the Institute for Advanced Study in Princeton, the University of Chicago, and the University of California, Berkeley. His distinctions include a Sloan Research Fellowship (2000), a Packard Fellowship (2001), the European Mathematical Society Prize (2004), and the Fields Medal winner (2006).

The work of Professor 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.