Abstract: It is about symmetric and skew-symmetric bilinear forms on vector spaces and vector bundles, Witt theory for algebraic varieties, Pontrjagin classes, Thom operators, and orientations on cohomology theories.

Abstract: H.Bohr's theory of almost periodic functions has numerous applications to various areas of mathematics. Two branches of this theory, both extending the classical setting of almost periodic functions on reals, were particularly rich on interesting and deep results: holomorphic almost periodic functions on tube domains and almost periodic functions on topological groups. This talk is devoted to a natural link between these two concepts - holomorphic almost periodic functions on coverings of complex manifolds, their function-theoretic properties and the `sprouts' of the theory of analytic sheaves on the corresponding Bohr compactifications of the coverings.

This is joint work with Alexander Brudnyi.