5 problems

Conjugacy-to-triangularity conjecture. For every $\phi\in\mathcal{E}_3(k)\cap\operatorname{T}_3(k)$, there exists $\sigma\in\operatorname{T}_3(k)$ such that

Rips's conjecture. Linear automorphisms, together with $\psi$, generate the entire tame automorphism group of $K[x_1,\ldots,x_n]$. The characteristic-zero analogue is known, while…

Let $Q$ be the affine quadric threefold and let $G$ be its tame automorphism group. Let $\mu$ be a symmetric atomic measure on $G$, let $\nu_n=\mu^{*n}$ be its $n$-fold convolution…

Let $k$ be a field of characteristic $0$, and let $3\leq p_1\leq d_2\leq d_3$ be integers with $p_1$ a prime number. Write $\mathrm{mdeg} F$ for the multidegree of a polynomial map…

Degree-two tameness conjecture. If