Thesis Defenses

2026

• Mikayel Mkrtchyan

  Date: Thursday, January 8, 2026 | 9:00am | Room: 2-449 | Zoom Link

  Committee: Zhiwei Yun, Wei Zhang, Benjamin Howard

  Higher Siegel-Weil formulae over function fields

  In their seminal work, Feng-Yun-Zhang introduced function field analogues of Kudla-Rapoport cycles for moduli spaces of shtukas, and initiated the study of their intersection theory. They proved a higher Siegel-Weil formula in the case of unitary groups and non-degenerate Fourier coefficients, relating the degrees of these cycles to higher derivatives of Siegel-Eisenstein series. In this talk, we will discuss two generalizations of their result: 1) we prove a higher Siegel-Weil formula for unitary groups for corank-1 degenerate coefficients, and 2) we introduce analogous special cycles on moduli spaces of symplectic shtukas, and prove a higher Siegel-Weil formula for such cycles in the non-degenerate case.