Infinite-dimensional Grassmannian and Weierstrass cycles in moduli spaces of algebraic curves

We estimate the dimensions of Weierstrass cycles in moduli spaces
of algebraic curves. (By definition Weierstrass cycles are cycles
specified   in terms of Weierstrass points.) Under certain conditions we
calculate  cohomology classes corresponding to these cycles in terms of
factorial Schur functions . We give also a series of relations in
tautological rings in terms of these functions.
Our calculations are based on the calculation of equivariant cohomology of
infinite-dimensional Grassmannian (we show that it can be identified with
the ring of shifted symmetric functions) and on consideration of the
Krichever embedding of moduli spaces into Grassmannian.

The results of the talk were obtained in collaboration with Frank Liou.