Stanislav Smirnov
Encyclopedia
Stanislav Konstantinovich Smirnov is a Russia
n mathematician
currently working at the University of Geneva
, who was awarded the Fields Medal
in 2010. His research focuses on the fields of complex analysis
, dynamical systems and probability theory
.
at Saint Petersburg State University
in 1992, where he worked under Victor Havin. His PhD
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. 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.
, 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.
s, with perfect scores and gold medals on both occasions. He has been awarded the St. Petersburg Mathematical Society
Prize (1997), the Clay Research Award
(2001), the Salem Prize
(joint with Oded Schramm
, 2001), the Göran Gustafsson Research Prize (2001), the Rollo Davidson Prize (2002), and the Prize of the European Mathematical Society
(2004).
In 2010 Smirnov was awarded the Fields medal
for his work on the mathematical foundations of statistical physics
, particularly finite lattice models. His citation read "for the proof of conformal invariance of percolation
and the planar Ising model
in statistical physics". In his laudation, Harry Kesten
said that Smirnov "has the talent and insight to produce surprising results, and his work has been a major stimulus for the explosion in the last 15 years or so of probabilistic results about random planar curves". After receiving the award, Smirnov expressed his wish to continue making important mathematical discoveries, saying "I look forward to proving more theorems. I hope the weight of this prize doesn't slow me down."
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
currently working at the University of Geneva
University of Geneva
The University of Geneva is a public research university located in Geneva, Switzerland.It was founded in 1559 by John Calvin, as a theological seminary and law school. It remained focused on theology until the 17th century, when it became a center for Enlightenment scholarship. In 1873, it...
, who was awarded the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 2010. His research focuses on the fields of complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, dynamical systems and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
.
Career
Smirnov attended a specialist mathematics school, Saint Petersburg Lyceum 239, until 1987. Smirnov completed his undergraduate degreeUndergraduate degree
An undergraduate degree is a colloquial term for an academic degree taken by a person who has completed undergraduate courses. It is usually offered at an institution of higher education, such as a university...
at Saint Petersburg State University
Saint Petersburg State University
Saint Petersburg State University is a Russian federal state-owned higher education institution based in Saint Petersburg and one of the oldest and largest universities in Russia....
in 1992, where he worked under Victor Havin. His PhD
PHD
PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...
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. Smirnov has held research positions at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
, the Max Planck Institute for Mathematics in Bonn
Bonn
Bonn is the 19th largest city in Germany. Located in the Cologne/Bonn Region, about 25 kilometres south of Cologne on the river Rhine in the State of North Rhine-Westphalia, it was the capital of West Germany from 1949 to 1990 and the official seat of government of united Germany from 1990 to 1999....
, and the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
. In 1998 he moved to the Royal Institute of Technology
Royal Institute of Technology
The Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for one-third of Sweden’s technical research and engineering education...
in Stockholm
Stockholm
Stockholm is the capital and the largest city of Sweden and constitutes the most populated urban area in Scandinavia. Stockholm is the most populous city in Sweden, with a population of 851,155 in the municipality , 1.37 million in the urban area , and around 2.1 million in the metropolitan area...
, and took up his current position as a professor in the Analysis, Mathematical Physics and Probability group at the University of Geneva
University of Geneva
The University of Geneva is a public research university located in Geneva, Switzerland.It was founded in 1559 by John Calvin, as a theological seminary and law school. It remained focused on theology until the 17th century, when it became a center for Enlightenment scholarship. In 1873, it...
in 2003.
Research
Smirnov is known best for his work on critical percolation theoryPercolation theory
In mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the article percolation.-Introduction:...
, in which he proved Cardy
John Cardy
John Lawrence Cardy FRS is a British theoretical physicist at the University of Oxford. He is best known for his work in theoretical condensed matter physics and statistical mechanics, and in particular for research on critical phenomena and conformal field theory.He was an undergraduate and...
'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
Oded Schramm
Oded Schramm was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution and for working at the intersection of conformal field theory and probability theory.-Biography:...
. He has obtained corresponding results of conformality for the random-cluster model and Ising model
Ising model
The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...
in two dimensions.
Awards
Smirnov was jointly ranked first in the 1986 and 1987 International Mathematical OlympiadInternational Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
s, with perfect scores and gold medals on both occasions. He has been awarded the St. Petersburg Mathematical Society
St. Petersburg Mathematical Society
The St. Petersburg Mathematical Society is a society of St. Petersburg mathematicians. It was dissolved and subsequently revived twice, each time changing its name:* St. Petersburg Mathematical Society...
Prize (1997), the Clay Research Award
Clay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...
(2001), the Salem Prize
Salem Prize
The Salem Prize, founded by the widow of Raphael Salem, is awarded every year to a young mathematician judged to have done outstanding work in Salem's field of interest, primarily the theory of Fourier series.-Past winners:...
(joint with Oded Schramm
Oded Schramm
Oded Schramm was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution and for working at the intersection of conformal field theory and probability theory.-Biography:...
, 2001), the Göran Gustafsson Research Prize (2001), the Rollo Davidson Prize (2002), and the Prize of the European Mathematical Society
European Mathematical Society
The European Mathematical Society is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians...
(2004).
In 2010 Smirnov was awarded the Fields medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
for his work on the mathematical foundations of statistical physics
Statistical physics
Statistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...
, particularly finite lattice models. His citation read "for the proof of conformal invariance of percolation
Percolation theory
In mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the article percolation.-Introduction:...
and the planar Ising model
Ising model
The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...
in statistical physics". In his laudation, Harry Kesten
Harry Kesten
Harry Kesten is an American mathematician best known for his work in probability, most notably on random walks and percolation theory.- Biography :...
said that Smirnov "has the talent and insight to produce surprising results, and his work has been a major stimulus for the explosion in the last 15 years or so of probabilistic results about random planar curves". After receiving the award, Smirnov expressed his wish to continue making important mathematical discoveries, saying "I look forward to proving more theorems. I hope the weight of this prize doesn't slow me down."