Alexandre Aleksandrovich Kirilloff (Russian: Алекса́ндр Алекса́ндрович Кири́ллов, born 1936) is a Soviet and Russian mathematician,[1] known for his works in the fields of representation theory, topological groups and Lie groups.

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 was published in 1962.

At the time he was the youngest Doctor of Science in the Soviet Union.

[3] Kirillov's son, Alexander Kirillov, Jr., is also a mathematician, working on the representation theory of Lie groups at the State University of New York at Stony Brook.