World Reputation Rankings 2015 results

r Education

The Times Higher Education has presented the World Reputation Rankings 2015 whose LIST contains the 100 most powerful global university brands by reputation.

The top ten positions are occupied by the 8 universities of USA and the 2 ones of United Kingdom.

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My 23 main mathematical theorems

As a mathematical and theoretical physicist, I have proved a lot of theorems and assertions. This is a LIST of my 23 most relevant original theorems:

• Modification of the abstract De Rham theorem
• Generalization of the Serra – Swan theorem for non-compact manifolds
• Serra – Swan-like theorem for graded manifolds
• Theorem on the cohomology of differential forms on an infinite order jet manifold
• Theorem on the cohomology of the variational bicomplex on fibre bundles
• Theorem on the cohomology of the Grassmann-graded variational bicomplex on graded bundles
• Solution of the global inverse problem of the calculus of variations in a very general setting
• Global variational formula
• First Noether theorem in a general setting of Grassmann-graded Lagrangians and their generalized  supersymmetries
• Theorem on the superpotential form of a gauge symmetry current in a general setting
• Theorem on the Koszul – Tate chain complex of higher-stage Noether identities of a generic differential operator on a fibre bundle
• Theorem on the Koszul – Tate chain complex of Noether identities of a generic reducible degenerate Grassmann-graded Lagrangian
• The inverse and direct second Noether theorems in a very general setting
• Theorem on the iterated BRST cohomology
• Theorem on the canonical decomposition of the jet bundle J^1C -> C of a bundle C of principal connections
• Comprehensive relations between Lagrangian and covariant (polysymplectic) Hamiltonian formalisms in a case of semiregular Lagrangians
• Conditions of a dynamic algebra to be a partially integrable system on a Poisson manifold
• Generalization of the Liouville – Arnold theorem on completely integrable systems to a case of partically integrable systems on a Poisson manifold and its non-compact invariant submanifolds
• Generalization of the Poincare – Lyapounov – Nekhoroshev theorem on partially integrable systems to a case of non-compact invariant submanifolds
• Theorem on global action-angle coordinates of partially integrable systems in a general case of invariant submanifolds which need not be compact
• Generalization of the Mishchenko – Fomenko theorem on superintegrable systems to a case of non-compact invariant submanifolds
• Theorem on global generalized action-angle coordinates of superintegrable systems in a case of possibly non-compact invariant submanifolds
• Theorem on reduction of a principal superbundle in the category of G-supermanifolds

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New book: Introduction to Global Variational Geometry

New book: Demeter Krupka, Introduction to Global Variational Geometry (Springer, 2015) (#)

The book is devoted to recent research in the global variational theory on smooth manifolds.

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