Time：16:00-17:00, Wednesday, November 4 2026
Venue：E14-215
Host： Huayi Chen, ITS
Speaker: Wei Zhang, Massachusetts Institute of Technology
Title：Arithmetic Diagonal Cycles and L-Functions
Abstract：The zeta function (or L-function) of an algebraic variety over a number field is conjectured to encode deep information about its algebraic cycles. We illustrate this paradigm by studying two types of "arithmetic diagonal cycles" on products of Shimura varieties: the diagonal cycle on the self-product of a Shimura variety and the graph cycle associated with the embedding of a Shimura subvariety of codimension one. In both cases, we present conjectures and theorems relating suitable arithmetic intersection numbers to the first derivatives of the relevant L-functions. We also discuss applications to the conjectures of Beilinson, Bloch, and Kato, which generalize the Birch and Swinnerton-Dyer conjecture for elliptic curves to higher-dimensional varieties.
