6 problems

Cyclicity conjecture. If $G_{\mathcal L}$ is finite, then $G_{\mathcal L}$ is cyclic.

Invariant D-module abelianization conjecture. The pull-back induces an isomorphism

Let $n\in\{8,16\}$, and let $L\subset\mathbb{R}_{sym}^{n\times n}$ be a subspace satisfying … and such that $\boldsymbol{\mathrm{P}}(L^\vee)\cap\boldsymbol{\mathrm{Z}}$ exists and…

Degree-zero word reformulation. The image of $w$ on $G$ must be

Let $K$ be an algebraically closed field of characteristic $0$, let $w(x_1,\dots,x_m)$ be a nontrivial group word, and let $\operatorname{PSL}_2(K)$ denote the projective linear gr…

Let $G$ be an infinite reductive group over a field of positive characteristic, and let $G^{0}$ denote its connected component. Assume that $G^{0}$ is not a torus. Infinite delta-i…