6 problems

Let $F$ be a number field and $\mathbb{A}$ its ring of adeles. Let $(V_n,q_n)\subset (V_{n+1},q_{n+1})$ be an inclusion of quadratic spaces over $F$ of dimensions $n$ and $n+1$, wi…

Let $F$, $\mathbb{A}$, $V_n$, $V_{n+1}$, $\operatorname{SO}_n$, and $\operatorname{SO}_{n+1}$ be as above, and let…

Let $H\simeq\operatorname{SO}(3)$ be the split special orthogonal group over $\mathbb{Q}$ and let $G\simeq\operatorname{SO}(4)$ be the quasi-split special orthogonal group over…

Let $G_n\subset G_{n+1}$ be the special orthogonal groups in the Gross–Prasad setting, and let $\pi_n$ and $\pi_{n+1}$ be the associated tempered cuspidal automorphic representatio…

Let $F$ be a number field with adèle ring $\mathbb{A}_F$, and let $V_n\subset V_{n+1}$ be quadratic spaces of dimensions $n$ and $n+1$ over $F$, with $n\geq 2$ and $V_n$ not a hype…

The HSOP conjecture. The traces of the following 14 words in $x$ and $y$ form an HSOP of ${\mathcal S}_5$: