9 problems

Howe's conjecture. For every compact subset $Omega\subset G(F)$ and every open subgroup $K\subset G(F)$, the restriction of $J(Omega)$ to $C_c(G(F)/K)$ is finite-dimensional.

Generalized convergence conjecture. The same convergence assertion should hold for any semisimple group $G$ with finite center and generic $n_0\in N$. This extension would generali…

Let $\Gamma$ be a geometrically finite group, let $\sigma$ be a representation parameter, let $\lambda\in{\mathfrak a}_{\mathbb C}^*$, and let $\varphi$ be the auxiliary parameter…

Uniqueness conjecture. The distribution $\pi_0$ is the unique stationary distribution of the gap sequence of the infinite Atlas model. The conjecture concerns the long-time behavio…

Let $G$ be a $p$-adic group, let $\mathcal K\subset\mathcal H(G)$ be the space of weightless functions, let $\mathcal E\subset\mathcal D^G$ be the distinguished space of invariant…

Let $F(P(N^{+}))$ be the space of smooth functions on the projective space $P(N^{+})$. In the three-dimensional case, choose … and equip this space with its nuclear topology. Conje…

Let $F$ be a local non-Archimedean field, let $G=\operatorname{GL}(n,F)$ with Lie algebra $\mathfrak{g}$, and let $\mathcal B$ be its Bruhat–Tits building. Fix an irreducible smoot…

Let $(R_1(t),R_2(t))$ be the reflected process in the nonnegative quadrant defined in (2.20) and (2.21), and let ${\bm\alpha}$ be the parameter satisfying…

Let $M$ be a closed, connected, orientable manifold, and let $X$ be a volume-preserving vector field on $M$. Write $\mathcal I_X(M)$ for the space of all $X$-invariant distribution…