Vladimir Solomonovich Retakh (russian: Ретах Владимир Соломонович; 20 May 1948) is a Russian-American mathematician who made important contributions to Noncommutative
algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
and
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...
among other areas.
Biography
Retakh graduated in 1970 from the
Moscow State Pedagogical University
Moscow State Pedagogical University or Moscow State University of Education is an educational and scientific institution in Moscow, Russia, with eighteen faculties and seven branches operational in other Russian cities. The institution had underg ...
. Beginning as an undergraduate Retakh regularly attended lectures and seminars at the
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
most notably the
Gelfand seminars. He obtained his PhD in 1973 under the mentorship of
Dmitrii Abramovich Raikov. He joined the Gelfand group in 1986.
His first position was at the central Research Institute for Engineering Buildings and later obtained his first academic position at the Council for Cybernetics of the Soviet Academy of Sciences in 1989. While at the Council for Cybernetics of the Soviet Academy of Sciences in 1990, Retakh had started working with
Gelfand on their new program on Noncommutative determinants. Prior to immigrating to the US in 1993 he also held a position at the
Research
Retakh's other contributions include:
* Contributions to the theory of
general hypergeometric function
In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by . The general hypergeometric function is a function that is (more or less) de ...
s
* Contributions to the theory of
Lie–Massey operators
* Instigated the study of homotopical properties of categories of extensions based on the Retakh isomorphism
* Introduction of noncommutative determinants, also known as
quasideterminant In mathematics, the quasideterminant is a replacement for the determinant for matrices with noncommutative entries. Example 2 × 2 quasideterminants are as follows:
:
\left, \begin
a_ & a_ \\
a_ & a_ \end
\_ = a_ ...
s
* Introduction of
noncommutative symmetric functions
* The introduction of noncommutative
Plücker coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3. Because they satisfy a quadratic constraint, they establish a one-to-o ...
* Noncommutative
integrable system
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first i ...
s
Recognition
He was included in the 2019 class of fellows of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...
"for contributions to noncommutative algebra and noncommutative algebraic geometry".
References
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{{DEFAULTSORT:Retakh, Vladimir
1948 births
Living people
Russian mathematicians
20th-century American mathematicians
Fellows of the American Mathematical Society