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9781470473556 Academic Inspection Copy

The Diverse World of PDEs

Algebraic and Cohomological Aspects
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This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13-17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frolicher structures in the formal Kadomtsev-Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.
I. S. Krasil'shchik, Independent University of Moscow, Russia. A. B. Sossinsky, Independent University of Moscow, Russia. A. M. Verbovetsky, Independent University of Moscow, Russia.
L. Amata and F. Oliveri, Automatic determination of optimal systems of Lie subalgebras: The package SymboLie O. D. Artemovych, D. L. Blackmore, R. A. Kycia, and A. K. Prykarpatski, New Dubrovin-type integrability theory applications of differential rings I. A. Bobrova and V. V. Sokolov, Non-abelian Painleve systems with generalized Okamoto integral A. Bocharov, Mathematical etudes on quantum computation D. Gurevich and Pavel Saponov, Quantum vector fields via quantum doubles and their applications H. M. Khudaverdian, Nonlinear homomorphisms of algebras of functions are induced by thick morphisms H. M. Khudaverdian and T. T. Voronov, On the Buchstaber-Rees theory of ``Frobenius $n$-homomorphisms'' and its generalization J. Kryczka, Differential calculus over graded commutative algebras and vector bundles with inner structures F. Pugliese, G. Sparano, and L. Vitagliano, Vinogradov's cohomological geometry of partial differential equations J.-P. Magnot, E. G. Reyes, and V. Rubtsov, Frolicher structures, diffieties, and a formal KP hierarchy G. Sharygin, Quasi-derivations on $U{\mathfrak{gl}}_n$ and the argument shift method P. Tempesta and G. Tondo, Polarization of generalized Nijenhuis torsions
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