nLab Alexandre Vinogradov
Alexander Mikhailovich Vinogradov (Александр Михайлович Виноградов, 1938-2019) was a Russian mathematician working in the geometric theory of differential equations, developing the theory of diffieties with applications to variational calculus.
In co-authorship with members of his seminar he published also under the pseudonym Jet Nestruev (cf. Nestruev 2002).
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A. M. Astashov et al. Alexandre Mikhailovich Vinogradov, Russian Mathematical Surveys 75 Number 2 (2020) 369 [doi:10.1070/RM9931]
Selected publications
On partial differential equations:
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A. M. Vinogradov, Local symmetries and conservation laws, Acta Appl. Math., Vol. 2, 1984, p. 21, MR85m:58192, doi
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A. M. Vinogradov, Symmetries and conservation laws of partial differential equations: basic notions and results, Acta Appl. Math., Vol. 15, 1989, p. 3. MR91b:58282, doi
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A. M. Vinogradov, Cohomological analysis of partial differential equations and secondary calculus, bookpage Translations of Mathematical Monographs 204, Amer. Math. Soc. 2001, 247 p.
On diffieties:
- Alexandre M. Vinogradov: Scalar differential invariants, diffieties and characteristic classes, in: Mechanics, Analysis and Geometry: 200 Years after (1991) 379-414 [MR92e:58244, doi:10.1016/B978-0-444-88958-4.50020-3]
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Gabriele Vezzosi, Alexandre M. Vinogradov, Infinitesimal Stokes’ formula for higher-order de Rham complexes, Acta Appl. Math. 49, N. 3 (1997), 311-329.
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Gabriele Vezzosi, Alexandre M. Vinogradov, On higher order analogues of De Rham cohomology, Diff. Geom. and Appl. 19 (2003), 29-59.
- Jet Nestruev: Smooth manifolds and Observables, Graduate Texts in Mathematics 220 Springer (2002, 2020) [doi:10.1007/978-3-030-45650-4, ISBN:0-387-95543-7, pdf]
Related entries
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