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P.E.Pushkar (Independent Uni. of Moscow), "Basics of topology"

• Differential forms, de-Rahm operator, closed and exact differential forms, cohomology (as coset spaces of closed forms over exact ones), examples.
• Boundaries of a manifold, closed manifolds, homology as a space of closed submanifolds modulo the boundaries, examples.
• Integration of differential forms over submanifolds, Newton-Leibniz-Stokes-Ostrogradsky-Gauss formula, pairing between homology and cohomology.
• Product of differential forms, differential forms as an example of graded differential algebra, product in cohomology.
•  Hodge star operator, Laplacian, harmonic forms as zero modes of the Laplacian, isomorphism between harmonic forms and cohomology.
• Massey operations in the theory of differential forms.

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• Complex structures on the real spaces, space of complex structures on  $R^{2n}$.
• Spinors in different dimensions.
• Pure spinors and the space of complex structures.
• Relation of the twistor space to the space-time.
• Holomorphic structures in twistor space as solutions of the field equations in space-time.

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• Yang-Mills (YM) theory, gauge fixing, ghosts, Batalin-Vilkovisky (BV) description.
• YM theory in the first order formalism in dimensions 2 and 4, zero coupling constant limit.
• Chern-Simons (CS) theory, gauge fixing, ghosts, BV description, YM theory at zero coupling constant in dimension 2 as a reduction of the CS theory.
• Perturbation theory in the CS theory and Massey operations.
• Holomorphic CS theory.
• Supersymmetric YM theories, maximal theory in 10 dimensions, its reduction to smaller dimensions.
• Holomorphic CS theory on twistor superspace and super YM with zero coupling constant.
• How to introduce a  non-zero coupling constant.

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• Anticommuting (fermionic) coordinates, Berezin integration over fermionic variables, integrals leading to determinants of quadratic forms, superspaces.
• Theory of differential forms in the superspace language, odd Fourier transformation and correspondence between forms and polyvector fields, reinterpretation of the Hodge star operation.
• BV master equation - pure, classical and quantum.
• BV as an odd Fourier transform for the theory of integration of differential forms.
• BV formalism as a generalization of the Faddeev-Popov gauge fixing.
• BV integral and BV effective action.
• Homotopy algebra equations as a solution of the classical BV equations.
• Summation of Feynman tree  diagrams and induced  homotopy algebra structures, Massey operations.

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• Berkovits' graded differential algebra.
• Cohomology in the Berkovits complex as fields in supersymmetric YM theory (in BV formalism).
• Massey operations and induced YM action on the Berkovits cohomology for a regular system of quadrics.

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• dilaton gravities from spherical reductions and from srings
• Poisson sigma models and integrability
• Hawking radiation in two dimensions
• noncommutative gravity (NC) in two dimensions
• quantum NC gravity

A.Strelchenko (Leipzig), "Polarization tensor of neutral gluons in condensate fields at  high temperature"