The diverse world of PDEs : Algebraic and cohomological aspects Publisher’s description: 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 Frölicher structures in the formal Kadomtsev Petviashvili hierarchy and computer based determination of optimal systems of Lie subalgebras.