# Fourier-Jacobi cycles and derivative of L-functions

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Yifeng Liu, Northwestern University
Fine Hall 214

In this talk, we construct the so-called Fourier-Jacobi cycles on unitary Shimura varieties. The height pairing of these cycles can be regarded as the arithmetic analogue of classical Fourier-Jacobi periods for the pair of unitary groups of equal rank.

We will propose a conjectural formula relating such height pairing and derivative of certain Rankin-Selberg L-function of symplectic type. We will also explain an approach toward this conjecture using arithmetic relative trace formula.