6 problems

Generator-number conjecture. The highest possible level of an orbit is $n+1$.

Smoothness conjecture. Orbits of points in Case 4 will consist of a countable number of copies of an interval $I$, the union of a number of subintervals $J_n$, in each of which the…

Let $G$ be a reductive group with involution $\theta$, let $K^*$ act on the symmetric variety $P=\{g^{-1}\theta(g)\mid g\in G\}$ by conjugation, and let … be the quotient morphism,…

Let $\mathcal{O}_1$ denote the principal orbit of the $B_4$-action on $\mathbb{P}^2(\mathbb{Q})$. Based on the observed orbit statistics, the three-quarter density conjecture. The…

Let $G$ be a reductive algebraic group with a Chevalley $\mathbb{Z}$-form $G_{\mathbb{Z}}$, and set … Let $(\star)$ be the condition on primes used in the paper, and let $d$ be def…

Let $G$ be the algebraic group under consideration, with Lie algebra $\mathfrak{g}$, and let $\mathbb{E}(r,\mathfrak{g})$ denote the variety of $r$-dimensional elementary abelian s…