9 problems

Let $\beta$ denote the Burau representation of the braid group on $n$ strands, let $q$ be a $d$-th root of unity, and let $\sigma$ denote the relevant braid-group generator. Write…

Let $B_n$ be the braid group on $n$ strands, let $\mathbb{E}$ be the relevant ordered field with quadratic form $Q$, and let … be the reduced Burau representation. A braid…

Let $\mathcal{O}_1$ be the principal orbit in $\mathbb{P}^2(\mathbb{Q})$, and let $\mathcal{Q}(p)$ be the set of quantizations of $p\in\mathcal{O}_1$ in…

Let $S_d$ be the set of positive rational numbers whose numerator and denominator are less than or equal to $d$ when written in irreducible form. For a subset $A$ of…

Let $F$ be the deviating subgroup associated with the image of the Burau representation of $B_3$, and let a group be free of countably infinite rank when it has a countably infinit…

Morier-Genoud–Ovsienko–Veselov conjecture. The specialised Burau representation $\widetilde{\rho}_\mu$ is faithful whenever $\mu$ lies outside the annulus

For a real number $x>0$, let $[x]_q$ denote the associated $q$-deformation and let $R(x)$ be the radius of convergence of its Taylor series. Write … for the golden ratio, and let…

Let $B_n$ be the braid group, let $\beta:B_n\to\Gamma$ be the unreduced Burau representation, and let $\beta':B_n\to\Gamma'$ be its reduced representation, where $\Gamma$ is the un…

Let $B_4$ be the braid group on four strands, let $\rho$ denote the representation used in the paper, and let $T_4$ be the object on which the braid acts. For a Laurent polynomial,…