Smirnov attended a specialist mathematics school, Saint St. Petersburg Lyceum 239, until 1987. Smirnov completed his undergraduate degree at Saint St. Petersburg State University in 1992, where he worked under Victor Havin. His Doctor of Philosophy was conducted at Caltech under advisor Nikolai G. Makarov.
His thesis was entitled Spectral Analysis of Julia Sets and he received his doctorate in 1996.
His research focuses on the fields of complex analysis, dynamical systems and probability theory. Smirnov has held research positions at Yale University, the Max Planck Institute for Mathematics in Bonn, and the Institute for Advanced Study in Princeton. In 1998 he moved to the Royal Institute of Technology in Stockholm, and took up his current position as a professor in the Analysis, Mathematical Physics and Probability group at the University of Geneva in 2003.
Smirnov is known best for his work on critical percolation theory, in which he proved Cardy"s formula for critical site percolation on the triangular lattice, and deduced conformal invariance.
The conjecture was proved in the special case of site percolation on the triangular lattice. Smirnov"s theorem has led to a fairly complete theory for percolation on the triangular lattice, and to its relationship to the Schramm–Loewner evolution introduced by Oded Schramm.
He has obtained corresponding results of conformality for the random-cluster model and Ising model in two dimensions.
American Mathematical Society.