Special cycles for unitary Shtukas and modularity

We define a generating series of algebraic cycles on the moduli stack of unitary Shtukas and conjecture that it is a Chow-group valued automorphic form. This is a function field analogue of the special cycles defined by Kudla and Rapoport, but with an extra degree of freedom namely the number of legs of the Shtukas. I will talk about several pieces of evidence for the conjecture. This is joint work with Tony Feng and Wei Zhang.