Algebra - geometrical and cohomological theory of nonlinear PDEs, differential calculus over commutative algebras and applications of these teories to mechanics and theoretical physics
Main publications:
A.M. Vinogradov, “Algebra logiki teorii lineinykh differentsialnykh operatorov”, Doklady Akademii Nauk SSSR, matematika, 205:5 (1972), 1025–1028
A.M. Vinogradov, “Nekotorye gomologicheskie sistemy, svyazannye s differentsialnym ischisleniem v kommutativnykh algebrakh”, Uspekhi matematicheskikh nauk, 34:6 (1979), 145–150
A.M. Vinogradov, “Geometriya nelineinykh differentsialnykh uravnenii”, VINITI, Akad. Nauk SSSR, ser. Problemy geometrii, 11 (1980), 89–134
A.M. Vinogradov, “The C-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory, II. The nonlinear theory”, J. Math. Anal. Appl., 100:1 (1984), 1–129
A.M.Vinogradov, Cohomological Analysis of Partial Differential Equations and Secondary Calculus,, Translations of Mathematical Monographs,, 204, American Mathematical Society, Providence, Rhode Island, USA, 2001
