Stanislav Smirnov

Stanislav Smirnov received the 2001 Clay Research Award "for establishing the existence of the scaling limit of two-dimensional percolation, and for verifying John Cardy's conjectured relation." Smirnov was born in Russia, educated at Saint Petersburg State University and the California Institute of Technology, and presently is a senior lecturer at the Royal Institute of Technology in Stockholm and a researcher at the Swedish Royal Academy of Science. He formerly held positions at Yale, the Max Planck Institute in Bonn, and the Institute for Advanced Study in Princeton. At age 30, he is also one of the leading experts in the field of complex dynamics, a branch of mathematics concerned with the iteration of certain types of maps and made famous by the analysis of the fractal sets that arise in the study of their attractors. "

A percolation process is a mathematical model that describes the random spread of a fluid through an ambient medium. Such models are frequently used to describe phenomena from the penetration of oil through porous rock to the spread of an infectious disease. Smirnov's insight concerning percolation processes on a two-dimensional lattice starts with the observation that one can exploit the symmetry of a triangular lattice to exhibit subtlety not understood on a square lattice. Taking advantage of this symmetry, he was able to establish a mathematical theory of the behavior as the size of the lattice tends to zero. John Cardy conjectured that in this limit the measure that determines the crossing probabilities exists and is conformally invariant. Moreover, Cardy predicted exact formulas for these limiting crossing probabilities. Smirnov has established Cardy's relation. Furthermore, combined with recent results of Lawler, Schramm, and Werner, it now appears possible to establish a number of conjectures in the physics literature concerning fractal dimensions for percolation.

Details of Stanislav Smirnov's results on percolation can be found in his article:

S. Smirnov. Critical Percolation in the Plane. I. Conformal invariance and Cardy's Formula. II. Continuum scaling limit. Copies can be downloaded in postscript or DVI format from http://www.math.kth.se/~stas/papers/index.html

Smirnov has also published many important and influential results in the field of complex dynamics. We mention just two recent papers: J. Graczyk, S. Smirnov. Non-uniform hyperbolicity in complex dynamics. (Also available from the above link).

J. Graczyk, S. Smirnov. Collet, Eckmann, and Holder. Invent. Math. 133 (1998), no. 1, 69-96.