Alexandre Kirillov
Encyclopedia
Alexandre Aleksandrovich Kirillov is a Soviet and Russia
n mathematician, renowned for his works in the fields of representation theory
, topological group
s and Lie group
s. In particular he introduced the orbit method into representation theory.
Kirillov studied at Moscow State University
where he was a student of Israel Gelfand
. His Ph.D.
(kandidat
) dissertation Unitary representations of nilpotent Lie groups 1962 was so successful that he was awarded the much higher degree of Doctor of Science
instead. At the time he was the youngest Doctor of Science in the Soviet Union
. He worked at the Moscow State University until 1994 when he became the Francis J. Carey Professor of Mathematics at the University of Pennsylvania
, where he still teaches as of 2010.
During his school years, Kirillov was a winner of many mathematics competitions, and he is still an active organizer of Russian mathematical contests. Kirillov is an author of many popular school-oriented books and articles.
Kirillov's son, Alexander Kirillov, Jr., is also a professional mathematician, working on the representation theory of Lie groups
at the State University of New York at Stony Brook
.
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, renowned for his works in the fields of representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
, topological group
Topological group
In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology. A topological group is a mathematical object with both an algebraic structure and a...
s and Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s. In particular he introduced the orbit method into representation theory.
Kirillov studied at Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
where he was a student of Israel Gelfand
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand was a Soviet mathematician who made major contributions to many branches of mathematics, including group theory, representation theory and functional analysis...
. His Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
(kandidat
Kandidat
The Candidate of Sciences degree is a first post-graduate scientific degree in some former Eastern Bloc countries, such as Russia and Ukraine, which is awarded for original research that constitutes a significant contribution to a scientific field. The degree was first introduced in the USSR on...
) dissertation Unitary representations of nilpotent Lie groups 1962 was so successful that he was awarded the much higher degree of Doctor of Science
Doctor of Science
Doctor of Science , usually abbreviated Sc.D., D.Sc., S.D. or Dr.Sc., is an academic research degree awarded in a number of countries throughout the world. In some countries Doctor of Science is the name used for the standard doctorate in the sciences, elsewhere the Sc.D...
instead. At the time he was the youngest Doctor of Science in the Soviet Union
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....
. He worked at the Moscow State University until 1994 when he became the Francis J. Carey Professor of Mathematics at the University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
, where he still teaches as of 2010.
During his school years, Kirillov was a winner of many mathematics competitions, and he is still an active organizer of Russian mathematical contests. Kirillov is an author of many popular school-oriented books and articles.
Kirillov's son, Alexander Kirillov, Jr., is also a professional mathematician, working on the representation theory of Lie groups
Representation of a Lie group
In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie...
at the State University of New York at Stony Brook
State University of New York at Stony Brook
The State University of New York at Stony Brook, also known as Stony Brook University, is a public research university located in Stony Brook, New York, on the North Shore of Long Island, about east of Manhattan....
.