13 problems

Let $F$ be a number field, let $n$ be a positive integer, and let $\pi$ and $\pi'$ be cuspidal automorphic representations of $\operatorname{GL}(n,\mathbb{A}_F)$. Suppose that…

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…

Let $(M^n,g)$ be a closed manifold with a generic metric, where $3\leq n\leq 7$. Consider a closed minimal hypersurface obtained by min-max methods and each of its components. Mult…

Let $\mathbb F$ be a non-archimedean local field, and let Theorem … is also true when $\mathbb F$ has characteristic $2$. The characteristic-two case is not covered by the argument…

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 $F$ be the totally real field and $D$ the quaternion algebra used to define $\mathrm{PGU}_2^D$. Let ${\mathscr A}_{\mathrm{cusp}}(\mathrm{PGU}_2^D)$ denote the space of cuspida…

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…

Kable's multiplicity-one conjecture. The multiplicity of every irreducible representation is at most one.

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: