** Hengfei Lu**

TIFR, Mumbai

November 16, 2017

**The Prasad conjecture for PGSp(4)**:
Period Problem is one of the most popular interesting problems
in recently years, such as the Gan-Gross-Prasad conjectures. In this talk, we mainly focus on the local period problems, so called the relative local Langlands programs. Given a quadratic local field extension $E/F$ and a quasi-split reductive group $G$ defined over $F$ with associated quadratic character $chi_G$, let $pi$ be a smooth representation of $G(E)$. Assume the Langlands-Vogan conjecture, Prof. Prasad gives a precise description for the dimension $dim Hom_{G(F)}(pi,chi_G)$. We verify this conjecture if $pi$ is a discrete series representation and G=PGSp(4).