Viktor Vladimirovich Wagner, also Vagner (russian: Виктор Владимирович Вагнер) (4 November 1908 – 15 August 1981) was a Russian
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, best known for his work in
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
and on
semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.
The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', ...
s.
Wagner was born in
Saratov
Saratov (, ; rus, Сара́тов, a=Ru-Saratov.ogg, p=sɐˈratəf) is the largest city and administrative center of Saratov Oblast, Russia, and a major port on the Volga River upstream (north) of Volgograd. Saratov had a population of 901,36 ...
and studied at
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 ...
, where
Veniamin Kagan
Veniamin Fyodorovich Kagan (russian: Вениами́н Фёдорович Ка́ган; 10 March 1869 – 8 May 1953) was a Russian and Soviet mathematician and expert in geometry. He is the maternal grandfather of mathematicians Yakov Sinai and ...
was his advisor. He became the first geometry chair at
Saratov State University
Saratov Chernyshevsky State University (russian: Саратовский государственный университет имени Н. Г. Чернышевского, СГУ, transcribed as SGU) is a major higher education and research inst ...
. He received the
Lobachevsky Medal
The Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky.
History
The Lobachevsky Prize was established ...
in 1937.
Wagner was also awarded "the
Order of Lenin
The Order of Lenin (russian: Орден Ленина, Orden Lenina, ), named after the leader of the Russian October Revolution, was established by the Central Executive Committee on April 6, 1930. The order was the highest civilian decoration b ...
, the
Order of the Red Banner
The Order of the Red Banner (russian: Орден Красного Знамени, Orden Krasnogo Znameni) was the first Soviet military decoration. The Order was established on 16 September 1918, during the Russian Civil War by decree of th ...
, and the title of Honoured Scientist RSFSR. Moreover, he was also accorded that rarest of privileges in the USSR: permission to travel abroad."
Wagner is credited with noting that the collection of
partial transformation
In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often bot ...
s on a set ''X'' forms a semigroup
which is a subsemigroup of the semigroup
of
binary relation
In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of ele ...
s on the same set ''X'', where the semigroup operation is
composition of relations
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation from two given binary relations ''R'' and ''S''. In the calculus of relations, the composition of relations is called relative multiplica ...
. "This simple unifying observation, which is nevertheless an important psychological hurdle, is attributed by Schein (1986) to V.V. Wagner."
[Peter M. Higgins (1992) ''Techniques of Semigroup Theory'', page 5, ]Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books ...
See also
*
Inverse semigroup In group theory, an inverse semigroup (occasionally called an inversion semigroup) ''S'' is a semigroup in which every element ''x'' in ''S'' has a unique ''inverse'' ''y'' in ''S'' in the sense that ''x = xyx'' and ''y = yxy'', i.e. a regular semig ...
*
Heap
Heap or HEAP may refer to:
Computing and mathematics
* Heap (data structure), a data structure commonly used to implement a priority queue
* Heap (mathematics), a generalization of a group
* Heap (programming) (or free store), an area of memory f ...
References
*
External links
*
*
Wagner's Biography– in Russian
{{DEFAULTSORT:Wagner, Viktor Vladimirovich
Soviet mathematicians
Moscow State University alumni
Differential geometers
Algebraists
20th-century Russian mathematicians
1908 births
1981 deaths