Alexandre Mikhailovich Vinogradov

From 1998 to 2019, Vinogradov organised and directed the so-called Diffiety Schools in Italy, Russia, and Poland, in which a wide range of courses were taught, in order to prepare students and young researchers to work on the theory of diffieties and secondary calculus.

Furthermore, Vinogradov introduced a new bracket on the graded algebra of linear transformations of a cochain complex. The Vinogradov bracket is skew-symmetric and satisfies the Jacobi identity modulo a coboundary. Vinogradov’s construction is a precursor of the general concept of a derived bracket on a differential Leibniz algebra introduced by Kosmann-Schwarzbach in 1996. These results were also applied to Poisson geometry.

In 1993 he was one of the promoters of the Schrödinger International Institute in Mathematical Physics in Vienna. In 1997 he organised the large conference Secondary Calculus and Cohomological Physics in Moscow, which was followed by a series of small conferences called Current Geometry that took place in Italy from 2000 to 2010.

Vinogradov was one of the initial founder of the mathematical journal Differential Geometry and its Applications, remaining one of the editors from 1991 to his last days. A special issue of the journal, devoted to the geometry of PDEs, was published in his memory.

Between the sixties and the seventies, inspired by the ideas of Sophus Lie, Vinogradov changed once more research interests and began to investigate the foundations of the geometric theory of partial differential equations. Having become familiar with the work of Spencer, Goldschmidt and Quillen on formal integrability, he turned his attention to the algebraic (in particular, cohomological) component of that theory. In 1972, he published a short note containing what he called the main functors of the differential calculus over commutative algebras.

From 1967 until 1990, Vinogradov headed a research seminar at Mekhmat, which became a prominent feature in the mathematical life of Moscow. In 1978, he was one of the organisers and first lecturers in the so-called People's University for students who were not accepted to Mekhmat because they were ethnically Jewish (he ironically called this school the “People’s Friendship University”). In 1985, he created a laboratory that studied various aspects of the geometry of differential equations at the Institute of Programming Systems in Pereslavl-Zalessky and was its scientific supervisor until his departure for Italy.

After teaching for one year at the Moscow Mining Institute, in 1965 he received a position at the Department of Higher Geometry and Topology of Moscow State University. He obtained his habilitation degree (doktorskaya dissertatsiya) in 1984 at the Institute of Mathematics of the Siberian Branch of the USSR Academy of Science in Novosibirsk in Russia. In 1990 he left the Soviet Union for Italy, and from 1993 to 2010 was professor in geometry at the University of Salerno.

Between 1955 and 1960 Vinogradov studied at the Mechanics and Mathematics Department of Moscow State University (Mech-mat). He pursued a PhD at the same institution, defending his thesis in 1964, under the supervision of V.G. Boltyansky.

Alexandre Mikhailovich Vinogradov (Russian: Александр Михайлович Виноградов; 18 February 1938 – 20 September 2019) was a Russian and Italian mathematician. He made important contributions to the areas of differential calculus over commutative algebras, the algebraic theory of differential operators, homological algebra, differential geometry and algebraic topology, mechanics and mathematical physics, the geometrical theory of nonlinear partial differential equations and secondary calculus.

A.M. Vinogradov was born on 18 February 1938 in Novorossiysk. His father, Mikhail Ivanovich Vinogradov, was a hydraulics scientist; his mother, Ilza Alexandrovna Firer, was a medical doctor. Among his more distant ancestors, his great-grandfather, Anton Smagin, was a self-taught peasant and a deputy of the State Duma of the second convocation.