Number Theory Seminar: Higher Siegel-Weil formula for unitary groups over function fields: case of corank-1 coefficients

The arithmetic Siegel-Weil formula relates degrees of special cycles on Shimura varieties to derivatives of certain Eisenstein series. In their seminal work, Feng-Yun-Zhang have defined analogous special cycles on moduli spaces of shtukas over function fields, and proved a higher Siegel-Weil formula relating degrees of special cycles on moduli spaces of shtukas with r legs, to r-th derivatives of non-degenerate Fourier coefficients of the Eisenstein series. In this talk, I will report on joint work with Tony Feng and Benjamin Howard, where we prove a higher Siegel-Weil formula for corank-1 singular Fourier coefficients. A key feature of the proof is an unexpected full support property of the relevant “Hitchin” fibration.