Voronov graduated from
Moscow State School 57 in 1980. He received an M.S. in Mathematics in 1985 and a Ph.D. in Mathematics at
Moscow State University in 1988 under
Yuri I. Manin. Alexander Voronov is known for his work on the super Mumford isomorphism (see
Mumford measure), semi-infinite cohomology, operads in quantum field theory (see
Swiss-cheese operad),
Deligne's and
Kontsevich's conjectures on Hochschild cohomology, cohomology of vertex operator algebras, and string topology (see
cactus operad). He is a Fellow of the
American Mathematical Society, an AMS Centennial Fellow,, a
Simons Fellow, and a 2010
Japan Society for the Promotion of Science (JSPS) Research Fellow. ==Selected publications==