Speaker: Professor Liang Xiao (University Connecticut)

Title: non-vanishing of central L-value versus vanishing of Selmer group: the case of unitary Gan-Gross-Prasad setting

Place and Time: Aug 17 Thursday, 4:00pm-5:00pm; South Building Room 817

Abstract:   The famous work of Kolyvagin shows that the non-vanishing of central value of the L-function associated to an elliptic curve implies the vanishing of its Selmer group. This was a key component in proving B-SD conjecture in the rank

zero and one case. I will report on a recent joint work-in-progress with Yifeng Liu, Yichao Tian, Wei Zhang, and Xinwen Zhu, on a generalization of Kolyvagin's theorem for automorphic forms on higher rank groups, in particular the case of unitary Gan-Gross-Prasad paradigm.