11 problems

Multiplicity one conjecture. Multiplicity one holds for restriction of irreducible admissible representations of $\widetilde{{\mathbf{G}}}(k)$ to ${\mathbf{G}}(k)$.

Let $E/F$ be a quadratic extension. Let $\pi$ be an irreducible representation of $\operatorname{GL}_{2n}(F)$, and let $\chi$ be a character of $E^{\times}$. Multiplicity-one conje…

Let $\mathcal C$ be a smooth projective curve over $\mathbb C$, let $G$ be a split connected semi-simple group, and let $\operatorname{Bun}$ be the moduli stack of principal $G$-bu…

Σ × σ multiplicity-one conjecture. With these notations,

Let $F$ be a $p$-adic field, let $\Pi$ be an irreducible selfdual representation of $G_2(F)$, let $\psi$ be a nontrivial additive character of $F$, and let $\widetilde\pi$ be an ir…

Let $F$ be a $p$-adic field, let $\Pi$ be an irreducible generic representation of $G_2(F)$, let $\psi$ be a nontrivial additive character of $F$, and let $\widetilde I(\chi,\psi)$…

Let $M^{n+1}$ be a closed manifold with a generic Riemannian metric, where $3\le n+1\le 7$. Consider closed minimal hypersurfaces obtained by min-max methods, and call a component…

Let $P$ be a parabolic subgroup with Levi component $M$, let $X_P$ be the associated spherical variety, and set $\mathcal{S}:=\mathcal{S}(X_P)$. Let…

Let $\overline{\rho}:G_F\rightarrow\operatorname{GL}_2(k)$ be an absolutely irreducible Galois representation, let $\mathfrak{m}$ be the associated maximal ideal, and let $d_F$ be…

Let $S_k(\Gamma_2)$ be the space of holomorphic Siegel cusp forms of weight $k$ for $\Gamma_2=\operatorname{Sp}_4(\mathbb{Z})$. Let $f_1,f_2\in S_k(\Gamma_2)$ be Hecke eigenforms,…

Uniqueness conjecture for Ginzburg–Rallis models. The Ginzburg–Rallis model on $V_{\mathbb D}$ is unique up to scalar: