2 problems

Polynomiality conjecture. There exists a polynomial $A_{\boldsymbol{\mu};\mathbf{d}}^{\mathbf{m}}(t)\in\mathbb{Z}[t]$ such that for every finite field $\mathbb{F}_q$ and every divi…

Let $G$ be a split reductive algebraic $\mathbb{C}$-group, and let $\mathfrak{X}_r(G)$ denote the character variety of a free group of rank $r$ in $G$. Polynomial-count conjecture.…