7 problems

Naidu–Rowell Property $F$ conjecture. The braid group representations associated with any object in a weakly integral braided fusion category have finite images.

Let $C_{0,4}$ be the four-punctured sphere, and consider the three basic pants decompositions whose separating contours separate respectively the pairs $(z_1,z_2)$, $(z_2,z_3)$, an…

Property $\mathrm{F}_\mathrm{braid}$ conjecture. A braided fusion category $\mathcal{B}$ has property $\mathrm{F}_\mathrm{braid}$ if and only if it is weakly integral.

Let $V$ be the two-dimensional vector space and let … with $\rho^R$ the associated representation of the necklace braid group $\mathcal{NB}_n$. For $n\geq 3$, the necklace braid gr…

Let $\Sigma$ be a closed surface of genus at least $2$, let $p=2r$ be an even integer, and consider the quantum representation … Here $V_p(\Sigma,n)$ is the vector space assigned b…

Let $S$ be the surface under consideration, let $\rho_p\colon \pi_1(S)\to \mathrm{PGL}_{d_p}(\mathbb{C})$ be the representations indexed by odd integers $p$, and let…

Let $B_n$ be the braid group on $n$ strands, and for each positive integer $k$ let $B_n[k]$ be the normal subgroup generated by $g_j^k$ for $1\leq j\leq n-1$. Squier's intersection…