Victor Anatolyevich Vassiliev
Encyclopedia
Victor Anatolyevich Vassiliev or Vasilyev , is a Soviet and Russia
n mathematician
. He is best known for his discovery of the Vassiliev invariants in knot theory
(also known as finite type invariants), which subsume many previously discovered polynomial knot invariant
s such as the Jones polynomial. He also works on singularity theory
, topology
, computational complexity theory
, integral geometry
, symplectic geometry, partial differential equations (geometry of wavefront
s), complex analysis
, combinatorics
, and Picard-Lefschetz theory.
until 1981.
From 1981 to 1987 he was a senior researcher at the Documents and Archives Research Institute, Moscow and a part-time mathematics teacher at Specialized Mathematical High School 57, Moscow.
In 1982 he defended his thesis under Vladimir Arnold
and received the title of Doctor
in 1992.
From 1987 to 1989 he was a senior researcher at the Statistical Information Systems Research Institute in Moscow.
From 1989 to 90 he was a senior researcher at the Department of Functional Analysis in the Institute of Applied Mathematics in Moscow.
From 1990 to 1995 he was a leading researcher at the Department of Mathematics in the Research Institute for System Studies in Moscow.
Since 1991 he has been professor at the Mathematics College of the Independent Moscow University.
Since 1997 he has been a principal researcher in the Department of Geometry and Topology at the Steklov Institute of Mathematics
in Moscow
He has been a visiting professor at the University of Paris
VII, and at the Mathematical Science Research Institute (MSRI) at the University of California, Berkeley
.
He was a visiting fellow commoner at Trinity College, Cambridge
in October–December 2000.
Vasilyev has been a member of the Russian Academy of Science since 2003 (corresponding member since 1997).
He is vice-chief editor of the Journal Functional Analysis and its Applications, and a board member of the Moscow Mathematical Society
.
In 1994 he was an invited speaker at the International Mathematical Congress in Zürich
(Plenary Address).
In 1986 he received the Moscow Mathematical Society Award.
He is married with three children.
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....
. He is best known for his discovery of the Vassiliev invariants in 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...
(also known as finite type invariants), which subsume many previously discovered polynomial knot invariant
Knot invariant
In the mathematical field of knot theory, a knot invariant is a quantity defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some invariants are indeed numbers, but invariants can range from the...
s such as the Jones polynomial. He also works on singularity theory
Singularity theory
-The notion of singularity:In mathematics, singularity theory is the study of the failure of manifold structure. A loop of string can serve as an example of a one-dimensional manifold, if one neglects its width. What is meant by a singularity can be seen by dropping it on the floor...
, 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...
, computational complexity theory
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other...
, integral geometry
Integral geometry
In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant transformations from the space of functions on one geometrical space to the...
, symplectic geometry, partial differential equations (geometry of wavefront
Wavefront
In physics, a wavefront is the locus of points having the same phase. Since infrared, optical, x-ray and gamma-ray frequencies are so high, the temporal component of electromagnetic waves is usually ignored at these wavelengths, and it is only the phase of the spatial oscillation that is described...
s), 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,...
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, and Picard-Lefschetz theory.
Biography
Vassiliev studied at the Faculty of Mathematics and Mechanics at the Lomonosov University in MoscowMoscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
until 1981.
From 1981 to 1987 he was a senior researcher at the Documents and Archives Research Institute, Moscow and a part-time mathematics teacher at Specialized Mathematical High School 57, Moscow.
In 1982 he defended his thesis under Vladimir Arnold
Vladimir Arnold
Vladimir Igorevich Arnold was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory,...
and received the title of Doctor
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
in 1992.
From 1987 to 1989 he was a senior researcher at the Statistical Information Systems Research Institute in Moscow.
From 1989 to 90 he was a senior researcher at the Department of Functional Analysis in the Institute of Applied Mathematics in Moscow.
From 1990 to 1995 he was a leading researcher at the Department of Mathematics in the Research Institute for System Studies in Moscow.
Since 1991 he has been professor at the Mathematics College of the Independent Moscow University.
Since 1997 he has been a principal researcher in the Department of Geometry and Topology at 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 Moscow
He has been a visiting professor at the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
VII, and at the Mathematical Science Research Institute (MSRI) at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
.
He was a visiting fellow commoner at Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
in October–December 2000.
Vasilyev has been a member of the Russian Academy of Science since 2003 (corresponding member since 1997).
He is vice-chief editor of the Journal Functional Analysis and its Applications, and a board member of the Moscow Mathematical Society
Moscow Mathematical Society
The Moscow Mathematical Society is a society of Moscow mathematicians aimed at the development of mathematics in Russia.The first meeting of the society was . Nikolai Brashman was the first president of MMO. Victor Vassiliev is the current president of MMO....
.
In 1994 he was an invited speaker at the International Mathematical Congress in Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
(Plenary Address).
In 1986 he received the Moscow Mathematical Society Award.
He is married with three children.