Theoretical and mathematical physicist Moscow State University, Lepage Research Institute400+ scientific publications including 28 books 110+ works reviewed in Mathematical Reviews 2450+non-self citations including 280+ in WikipediA

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My 23 main mathematical theorems

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Top results: 1) Gauge gravitation theory on natural bundles where gravity is a classical Higgs field. 2) Geometric formulation of classical field theory, including: (i) the differential calculus and a variational bicomplex on graded manifolds, (ii) Lagrangian formalism of even and odd variables on graded bundles, (iii) Noether theorems in a very general setting of reducible degenerate Lagrangian systems, (iv) BRST-extended Lagrangian field theory with higher-stage antifields and ghosts. 3) Covariant Hamiltonian field theory on polysymplectic manifolds. 4) Classical Higgs field theory on composite bundles. 5) Geometric formulation of non-relativistic time-dependent mechanics on fibre bundles over R. 6) Its quantization in a form of geometric quantization of symplectic foliations. 7) Geometric formulation of relativistic mechanics in terms of jets of one-dimensional submanifolds. 8) Extension of the Liouville - Arnold, Nekhoroshev and Mishchenko - Fomenko theorems on integrable Hamiltonian systems to a general case of not necessary compact invariant submanifolds.

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Gravitation Gauge Theory at Sardanashvily on Facebook

Beig a pseudo-Riemannian metric from the mathematical viewpoint, gravity by its physical nature is a classical Higgs field. A conjecture is that, being a Higgs field, a metric gravitational field is not quantized, but it is classical in principle.

Course of Theoretical Physics: TheorMinimum-XXI in Russian and at Sardanashvily on Facebook in Russian

This Course is alternative to the well-known Course of Theoretical Physics by Lev Landau in the middle of XX century. Its five volumes provide contemporary geometric and algebraic topological methods in field theory, quantum theory, and mechanics.