Wikinventia — Atlas of discoveries and inventions · Digital Age

Conformal invariance in critical percolation — Stanislav Smirnov

2001 AD · Transmission: Global
MathematicsTheoryRussian

Stanislav Smirnov proves in 2001 the conformal invariance of the critical percolation model on the triangular lattice, rigorously confirming Cardy's formula, predicted heuristically by physicist John Cardy in 1992 from statistical-physics arguments with no complete mathematical proof. The result precisely connects probability theory with complex analysis via discrete holomorphic functions, and represents one of the central advances in the rigorous foundation of conformal field theory applied to two-dimensional statistical systems. Smirnov received the Fields Medal in 2010.

InstitutionUniversity of Geneva
Historical regionRussia / Switzerland
Primary sourceSmirnov, S. — "Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits" (Comptes Rendus de l'Académie des Sciences, 333, 2001)
Secondary sourceInternational Mathematical Union — Fields Medal citation 2010
Original languageFrench/English
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