**Alexandre Kirillov** is a Russian mathematician, known for his works in the fields of representation theory, topological groups and Lie groups.

- In 1961 a seminar on representation theory was set up at the university and Kirillov became a member of this seminar from its initiation.
- Kirillov continued working at Moscow State University after the award of his doctorate, being made a professor in 1965.
- In 1966 the International Congress of Mathematicians was held in Moscow and again Kirillov was invited to lecture - he gave the lecture Theory of group representations which was published in the Proceedings.
- The editor-in-chief of the journal (holding this role from the founding of the journal) was his former thesis advisor Israil Moiseevic Gelfand, and both Kirillov and Gelfand continued to hold these roles on the editorial board until 1988 when Kirillov took over as editor-in-chief.
- Kirillov published a series of important papers in Functional Analysis and Applications.
- In 1972 Kirillov published his classic textbook (written in Russian) Elements of the Theory of Representations.
- At the International Congress of Mathematicians held in Helsinki in August 1978 Kirillov was an invited speaker - it was the third International Congress of Mathematicians which he had been invited to address and he gave the lecture Infinite-dimensional groups, their representations, orbits, invariants.
- In 1993 Kirillov published the text with the interesting title What is a number?
- Kirillov continued to hold the position of Professor of Mathematics at Moscow State University until 1995.
- Kirillov published Lectures on the orbit method in Russian in 2001 and in English in 2004.
- In 2006, Kirillov reached 70 years of age and a number of journals on whose editorial boards he had served produced volumes in his honour.
- Kirillov's orbit method, the Kirillov-Kostant bracket, Kirillov's character formula, the Gelfand-Kirillov conjecture, the Gelfand-Kirillov dimension, Kirillov's model, are terms firmly established in the language of mathematics.
- Kirillov's orbit method is one of the most original and fruitful discoveries in representation theory in its hundred-plus year history.
- Another fundamental direction was called to life by the seminal joint papers of Gelfand and Kirillov on the skew fields of fractions of universal enveloping algebras.
- Wonderful and as always highly original results were obtained by Kirillov in the theory of infinite-dimensional Lie groups and algebras, and their representations.
- Kirillov's seminar at Moscow State University gathered for 30 years.
- Kirillov has numerous students that were formed not only by the problems he put forward, but even more by his powerful personality.
- Alexander Kirillov has the gift of creating a specific atmosphere that stimulates research and has exquisite mathematical taste.
- We should mention that Andrei Yuryevich Okounkov, who was awarded a Fields medal in 2006, was a student of Kirillov and was introduced to leading edge research in Kirillov's seminar in Moscow.
- Finally note that Kirillov's son, Alexander Kirillov Jr, is a mathematician undertaking research on the representation theory of Lie groups at the State University of New York at Stony Brook.

Born 9 May 1936, Moscow, USSR, (now Russia).

View full biography at MacTutor

Origin Russia

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive