12 problems

Let $F$ be as in the linear-period setting, let $G=\mathrm{GL}_m(D)$, let $E/F$ be quadratic, let $H$ be the centralizer of $E^\times$ in $G$, and let $m_\mathrm{geom}(\pi,\chi)$ b…

Sakellaridis–Venkatesh conjecture. A relative discrete series representation $\pi$ in $L^2(X)$ is contained in an Arthur packet corresponding to an $X$-distinguished $A$-parameter

Let $Q=LU$ be a parabolic subgroup of $G$, let $N_L$ be a maximal unipotent subgroup of $L$, set $N=N_LU$, and let $\xi_L$ be a generic character of $[N_L]$, extended trivially acr…

Relative Poisson summation conjecture. One can choose these Schwartz spaces so that (FT1), (FT2'), (FT3), (basic:norm), (rapidlydecreasing), (Frechet), (nA:ratio), (Arch:ratio), an…

Let $\X$ be a symmetric variety and let the construction of an endoscopic variety associated to $\X$ be as in the paper. Endoscopic-variety conjecture. This construction should pla…

Let $\tilde{\mathbf G}$ be the twisted group in the Shalika-period setting, let $\omega$ be the specified central character, and let $\mathcal{C}(\tilde{G},\omega)$ be the strongly…

Let $G=\mathrm{GL}_m(D)$, let $H$ be the subgroup defining the linear period, let $\omega$ be a central character, and let $\mathcal{C}(G(F),\omega)$ be the corresponding Schwartz–…

Geometric epsilon-factor conjecture. Under these hypotheses,

Let $\mathfrak X$ be the global spherical period space associated with $X$, let $\mathcal L_k$ be the global Langlands group, and let ${^LG_X}\to {^LG}$ be the dual-group map. Let…

Buttcane's conjecture. Let $g$ be holomorphic with rapid decay on an open tube domain in $\mathfrak{a}^*_{\mathbb{C}}$ containing $\mathfrak{a}^*$, let $t\in G(\mathbb{R})$, let…

Let $\mathfrak s$ and $\mathfrak s'$ be the tangent spaces of the relevant symmetric spaces, equipped with the smooth-transfer relation defined by the transfer factor $\kappa$, and…

Let $k$ be a number field with adele ring ${\mathbb A}$, let ${\mathbf G}={\operatorname{GL}}_{2n}$ and ${\mathbf H}={\operatorname{GL}}_n\times{\operatorname{GL}}_n$ embedded diag…