Arithmetic Geometry and Number Theory RTG Seminar: On the Kudla-Rapoport conjecture

Seminar | November 4 | 3:10-5 p.m. | 740 Evans Hall

 Chao Li, Columbia

 Department of Mathematics

The Kudla-Rapoport conjecture predicts a precise identity between the arithmetic intersection numbers of special cycles on unitary Rapoport-Zink spaces and the derivatives of local representation densities of hermitian forms. It is a key local ingredient to establish the arithmetic Siegel-Weil formula, relating the height of generating series of special cycles on Shimura varieties to the derivative of Eisenstein series. We discuss a proof of this conjecture and global applications. This is joint work with Wei Zhang.

In the pretalk, I will review the theory of binary quadratic forms and illustrate its link to modular forms and intersection theory. I will discuss the classical formulas of Jacobi, Hurwitz and Gross-Keating, from the perspective of the Siegel-Weil formula.