Oleg Viro
Encyclopedia
Oleg Viro (b. 13 May 1948, Leningrad
, USSR
) is a mathematician
in the fields of topology
and algebraic geometry
, most notably real algebraic geometry
, tropical geometry
and knot theory
.
Viro's main invention in algebraic geometry is the "patchworking" technique, which allows real algebraic varieties
to be constructed by a sort of "cut and paste" method. Using this technique, Viro was able to complete the isotopy
classification of non-singular plane projective curves of degree 7. The patchworking technique was one of the fundamental ideas which motivated the development of tropical geometry
. In topology
, Viro is most known for his joint work with Vladimir Turaev, in which the Turaev-Viro invariants and related topological quantum field theory
notions were introduced.
Viro was an invited speaker at the International Congress of Mathematicians
in 1983 (Warsaw
) and the European Congress of Mathematicians in 2000 (Barcelona
). He is a recipient of the Goran Gustafsson Prize (1997) from the Swedish government.
Viro studied at the Leningrad State University where he received Ph.D. degree in 1974; his advisor was Vladimir Rokhlin. Viro taught from 1973 until 1991 at Leningrad State University. Since 1986 he is a member of the Saint Petersburg Department
of the Steklov Institute of Mathematics
. In 1992-1997, Viro was a F. B. Jones chair professor in Topology at the University of California, Riverside
.
In 1994-2007 he was a professor at Uppsala University
, Sweden
. On 8 February 2007, Viro and his colleague Burglind Juhl-Jöricke were forced to resign from the university. There had been a history of conflict at the Mathematics Institute, with allegations of disagreeable behavior by several parties in the conflict. A number of Swedish, European and American mathematicians protested the manner in which the two Professors of Mathematics were forced to resign. These protests include the following:
As of 2009, Viro is a senior researcher at the St. Petersburg Department of the Steklov Institute of Mathematics, and a Professor at Stony Brook University.
Viro is married to Julia Viro; they have a daughter, Polina, and a son, Ivan.
Leningrad
Leningrad is the former name of Saint Petersburg, Russia.Leningrad may also refer to:- Places :* Leningrad Oblast, a federal subject of Russia, around Saint Petersburg* Leningrad, Tajikistan, capital of Muminobod district in Khatlon Province...
, USSR
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
) is a 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....
in the fields of topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, most notably real algebraic geometry
Real algebraic geometry
In mathematics, real algebraic geometry is the study of real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them ....
, tropical geometry
Tropical geometry
Tropical geometry is a relatively new area in mathematics, which might loosely be described as a piece-wise linear or skeletonized version of algebraic geometry. Its leading ideas had appeared in different guises in previous works of George M...
and knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
.
Viro's main invention in algebraic geometry is the "patchworking" technique, which allows real algebraic varieties
Algebraic variety
In mathematics, an algebraic variety is the set of solutions of a system of polynomial equations. Algebraic varieties are one of the central objects of study in algebraic geometry...
to be constructed by a sort of "cut and paste" method. Using this technique, Viro was able to complete the isotopy
Homotopy
In topology, two continuous functions from one topological space to another are called homotopic if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions...
classification of non-singular plane projective curves of degree 7. The patchworking technique was one of the fundamental ideas which motivated the development of tropical geometry
Tropical geometry
Tropical geometry is a relatively new area in mathematics, which might loosely be described as a piece-wise linear or skeletonized version of algebraic geometry. Its leading ideas had appeared in different guises in previous works of George M...
. In topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, Viro is most known for his joint work with Vladimir Turaev, in which the Turaev-Viro invariants and related topological quantum field theory
Topological quantum field theory
A topological quantum field theory is a quantum field theory which computes topological invariants....
notions were introduced.
Viro was an invited speaker at the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in 1983 (Warsaw
Warsaw
Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...
) and the European Congress of Mathematicians in 2000 (Barcelona
Barcelona
Barcelona is the second largest city in Spain after Madrid, and the capital of Catalonia, with a population of 1,621,537 within its administrative limits on a land area of...
). He is a recipient of the Goran Gustafsson Prize (1997) from the Swedish government.
Viro studied at the Leningrad State University where he received Ph.D. degree in 1974; his advisor was Vladimir Rokhlin. Viro taught from 1973 until 1991 at Leningrad State University. Since 1986 he is a member of the Saint Petersburg Department
St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences
The St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences for "Петербургское отделение Математического института", Petersburg Department of the Mathematical Institute) is a mathematical research institute in St. Petersburg, part of the Russian Academy of...
of the Steklov Institute of Mathematics
Steklov Institute of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute is a research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. It was established April 24, 1934 by the decision of the General Assembly of the Academy of Sciences of the USSR in...
. In 1992-1997, Viro was a F. B. Jones chair professor in Topology at the University of California, Riverside
University of California, Riverside
The University of California, Riverside, commonly known as UCR or UC Riverside, is a public research university and one of the ten general campuses of the University of California system. UCR is consistently ranked as one of the most ethnically and economically diverse universities in the United...
.
In 1994-2007 he was a professor at Uppsala University
Uppsala University
Uppsala University is a research university in Uppsala, Sweden, and is the oldest university in Scandinavia, founded in 1477. It consistently ranks among the best universities in Northern Europe in international rankings and is generally considered one of the most prestigious institutions of...
, Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
. On 8 February 2007, Viro and his colleague Burglind Juhl-Jöricke were forced to resign from the university. There had been a history of conflict at the Mathematics Institute, with allegations of disagreeable behavior by several parties in the conflict. A number of Swedish, European and American mathematicians protested the manner in which the two Professors of Mathematics were forced to resign. These protests include the following:
- an open letter by Lennart CarlesonLennart CarlesonLennart Axel Edvard Carleson is a Swedish mathematician, known as a leader in the field of harmonic analysis.-Life:He was a student of Arne Beurling and received his Ph.D. from Uppsala University in 1950...
, former president of the International Mathematical UnionInternational Mathematical UnionThe International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...
, - a letter by Ari LaptevAri LaptevAri Laptev is a mathematician working on the spectral theory of partial differential equations.His PhD was obtained in 1978 at Leningrad State University under the supervision of Michael Solomyak....
, current president of the European Mathematical SocietyEuropean Mathematical SocietyThe 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...
, and - a letter from Salah Baouendi, Arthur JaffeArthur JaffeArthur Jaffe is an American mathematical physicist and a professor at Harvard University. Born on December 22, 1937 he attended Princeton University as an undergraduate obtaining a degree in chemistry, and later Clare College, Cambridge, as a Marshall Scholar, obtaining a degree in mathematics...
, Joel LebowitzJoel LebowitzJoel L. Lebowitz is a mathematical physicist widely acknowledged for his outstanding contributions to statistical physics, statistical mechanics and many other fields of Mathematics and Physics...
, Elliott H. LiebElliott H. LiebElliott H. Lieb is an eminent American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis....
and Nicolai ReshetikhinNicolai ReshetikhinNicolai Yuryevich Reshetikhin is a mathematical physicist, currently a professor of mathematics at the University of California, Berkeley and a professor of mathematical physics at the University of Amsterdam. His research is in the fields of low-dimensional topology, representation theory, and...
.
As of 2009, Viro is a senior researcher at the St. Petersburg Department of the Steklov Institute of Mathematics, and a Professor at Stony Brook University.
Viro is married to Julia Viro; they have a daughter, Polina, and a son, Ivan.