In earlier work we defined a theta series of algebraic cycles on the moduli space of unitary Shtukas with an arbitrary number of legs. This can be viewed as a generalization of theta series and arithmetic theta series for function fields. A main open problem after this construction is the modularity of the higher theta series. In this talk, I will explain a proof of the modularity of higher theta series when restricted to the generic fiber. This is joint work with Tony Feng and Wei Zhang.

Rational Cherednik algebras are (a degenerate version of) generalizations of Hecke algebras. We will construct finite-dimensional representations of these algebras from the cohomology of affine Springer fibers and Hitchin fibers with extra symmetry. We will also give a dimension formula for these representations. This is joint work with A.Oblomkov.