6 problems

Bump–Friedberg–Ginzburg's period conjecture. The expected lift from the 3-fold cover of $\operatorname{SL}_3$ to $\operatorname{PGL}_3$ is detected by a period involving an automor…

Let $G^*$ be the group with unipotent subgroup $N$, let $X$ be the relative space with open orbit $X_\emptyset$, and let $e_\emptyset^*$ denote restriction to the open orbit. Let…

Isomorphism conjecture. In the Archimedean case, this push-forward map is an isomorphism.

Let $E/F$ be a quadratic extension of local fields, let $v$ be a place of $F$, and let $G=U(W)\times U(V)$ and $G'$ be the corresponding local groups. Let…

Let $F$ be a number field, let $E/F$ be a quadratic extension, and let $v$ be a place of $F$. Let $G$ and $G'$ be the local groups in Zhang's comparison of relative trace formulas,…

Let $F_v$ be a local field, let $G(F_v)$ and $G'(F_v)$ be the groups in the source, and let $\pi_v=\pi_{n,v}\otimes\pi_{n+1,v}$ be an irreducible tempered unitary representation wi…