Speaker: Zeyu Wang (MIT)

Title: Intersection number of Rankin—Selberg cycles on Shtukas

Abstract: The Rankin—Selberg integral formula (for G = GL_n∗ GL_n−1 and
H = GL_n−1) is a formula relating integrals of Hecke eigenforms of
G along H to the L-function of the corresponding Galois represen-
tation (called the Rankin—Selberg L-function). In this talk, I will
introduce a generalization of this formula over function fields in
the everywhere unramified setting, relating self-intersection num-
bers of Rankin—Selberg cycles on the moduli of G-Shtukas to
higher derivatives of the Rankin—Selberg L-function. This gener-
alized formula can be regarded as a higher-dimensional analogue
of Yun—Zhang’s higher Gross—Zagier formula.