linear differential operators; jets; differential forms; commutative algebras.
Subject:
Algebraic theory of linear differential equations, including non-commutative and graded situations. Geometry, symmetries and conservation laws of partial differential equations and equations of mathematical physics.
Main publications:
On multiple generalizations of Lie algebras and Poisson manifolds, Secondary Calculus and Cohomological Physics // Contemporary Mathematics, v. 219, American Mathematical Society, 1998, (with A. M. Vinogradov).
Field extensions and extensions of linear differential operators // Acta Applicandae Mathematicae. V. 49, no. 3, December 1997. P. 271–280.
Residues without duality // Acta Applicandae Mathematicae. V. 49, no. 3, December 1997. P. 281–291.
Remarks on algebraic Lagrangian formalism // Acta Applicandae Mathematicae. V. 49, no. 3, December 1997, P. 331–338.
M. M. Vinogradov, “Co-connections and integral forms”, Dokl. Akad. Nauk, 338:3 (1994), 295–297; Dokl. Math., 50:2 (1995), 229–233
1991
2.
M. M. Vinogradov, “On a general algebraic theory of linear differential operators. I”, Dokl. Akad. Nauk SSSR, 317:2 (1991), 275–279; Dokl. Math., 43:2 (1991), 355–359
1989
3.
M. M. Vinogradov, “Fundamental functors of differential calculus in graded algebras”, Uspekhi Mat. Nauk, 44:3(267) (1989), 151–152; Russian Math. Surveys, 44:3 (1989), 220–221
M. M. Vinogradov, “Extensions of fields and extensions of linear differential operators”, Mat. Zametki, 30:2 (1981), 237–248; Math. Notes, 30:2 (1981), 606–612
1980
5.
M. M. Vinogradov, “The theory of residues in commutative algebras”, Uspekhi Mat. Nauk, 35:2(212) (1980), 203–204; Russian Math. Surveys, 35:2 (1980), 263–264
1978
6.
M. M. Vinogradov, “On de Rham and Spencer algebraic cohomology of smooth manifolds”, Dokl. Akad. Nauk SSSR, 242:5 (1978), 989–992
2020
7.
A. M. Astashov, I. V. Astashova, A. V. Bocharov, V. M. Buchstaber, V. A. Vassiliev, A. Verbovetsky, A. M. Vershik, A. P. Veselov, M. M. Vinogradov, L. Vitagliano, R. F. Vitolo, Th. Th. Voronov, V. G. Kac, Y. Kosmann-Schwarzbach, I. S. Krasil'shchik, I. M. Krichever, A. P. Krishchenko, S. K. Lando, V. V. Lychagin, M. Marvan, V. P. Maslov, A. S. Mishchenko, S. P. Novikov, V. N. Rubtsov, A. V. Samokhin, A. B. Sossinsky, J. Stasheff, D. B. Fuchs, A. Ya. Khelemsky, N. G. Khor'kova, V. N. Chetverikov, A. S. Schwarz, “Alexandre Mikhailovich Vinogradov (obituary)”, Uspekhi Mat. Nauk, 75:2(452) (2020), 185–190; Russian Math. Surveys, 75:2 (2020), 369–375
