Kapranov graduated from Lomonosov University in 1982 and received his doctorate in 1988 under the supervision of Yuri Manin at the Steklov Institute in Moscow.
In October 1998, Carlos Simpson published on arXiv the article “Homotopy Types of Strict 3-groupoids”,[4] which argued that the main result of the “
[5] Kapranov was also involved in the beginning of Voevodsky's program for the development of motivic cohomology.
With Israel Gelfand and Andrei Zelevinsky, Kapranov investigated generalized Euler integrals,
[6][7][8][9] According to Gelfand, Kapranov, and Zelevinsky: ... in an 1848 note on the resultant, Cayley ... laid out the foundations of homological algebra.
[10]In 1995 Kapranov provided a framework for a Langlands program for higher-dimensional schemes,[11] and with, Victor Ginzburg and Éric Vasserot, extended the "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces.
In 1998 Kapranov was an Invited Speaker with talk Operads and Algebraic Geometry at the International Congress of Mathematicians in Berlin.