7 problems

Let $S$ be the surface with fundamental group $\pi_1(S)$, let $G^{\mathbb{C}}$ be a complex semisimple Lie group, and let $\rho$ be a $G^{\mathbb{C}}$-quasi-Fuchsian representation…

Banach-algebra linearity conjecture. The condition

Exponential analytic functional conjecture. The algebra

Let $G$ be a reductive group acting on a complex manifold $Y$. Assume that $Y$ is $G$-Oka and let $X$ be a Stein $G$-manifold. The $G$-homotopy Runge property is the equivariant an…

Let $G$ be a reductive complex Lie group acting on a Stein manifold $X$ and on a complex manifold $Y$. Suppose that $Y$ is $G$-Oka, meaning that it has the equivariant Oka property…

Let $G_0$ be connected and let it be a complex group viewed as a real Lie group. Write $G\cong G_0\times G_0$, $K\cong G_0$, and identify $\mathfrak{s}$ with $\mathfrak{g}_0$, with…

Let $P$ be a complex Lie group and let $\boldsymbol{\pi}$ be a discrete cocompact subgroup, so that $P/\pi$ is a compact quotient. Invariant-structure conjecture. Every holomorphic…