3 problems

Linearization conjecture. Every such action should be conjugate to a linear action, equivalently, the acting subgroup should be conjugated into $\operatorname{GL}_n({\mathbb C})$.…

Let $F_n=\mathbb{K}\langle x_1,\ldots,x_n\rangle$ be the free associative algebra, and let $\mathbb{T}_{n-1}$ act effectively on $F_n$. Free associative Białynicki-Birula conjectur…

Let an effective regular action of a torus on an affine space be given. General linearization conjecture. Every such action on every affine space should be linearizable. The source…