My research interests are in noncommutative geometry, homological algebra, category theory and mathematical physics. Most of the problems I am working on are motivated by questions in mathematical physics. The approaches to these problems often involve the elaborate technique of higher algebraic structures such as homotopy algebras, higher operads, and higher categories. The solutions of these problems are applied to questions in Lie theory, algebraic geometry, and algebraic topology.
I came from a family of mathematicians.
Few articles of my father Alexandr N. Dolgushev are available on MathSciNet.
An article of my mother Nadezda V. Dolgusheva is also available on MathSciNet.