6 problems

Friedlander–Milnor reformulation. The Friedlander–Milnor conjecture for $\operatorname{SL}_2$ over $\overline{\mathbb{Q}}$ can be reformulated as

Yengui's stability conjecture. Every matrix $\sigma(x)\in \operatorname{SL}_n(R[x])$ is congruent to $\sigma(0)$ modulo $E_n(R[x])$; equivalently, there exists $E\in E_n(R[x])$ suc…

Let $R_k(\sigma,\Delta,\chi)$ denote the parameterized irreducible representations used in the source, where $k$, $\sigma$, $\Delta$, and $\chi$ are the associated parameters; let…

Let $SL_2(\mathbb Z/p\mathbb Z)$ denote the special linear group over the finite field with $p$ elements, and consider random sets of generators, with the relevant notion of random…

Let $r\geq 2$, let $n$ be a positive integer, and let $q$ satisfy $\gcd(q,n)=1$. Consider the quotient variety $\mathfrak{Q}_r(\operatorname{SL}_n(\mathbb{F}_q))$ and let $N$ denot…

Sah's homology stability conjecture. This homomorphism should be an isomorphism if $t\geq n+1$ and surjective if $t=n$.