3 problems

Let $\mathcal{T}$ be a triangulated category admitting a full exceptional sequence of length $n$, and let $\mathfrak{B}_n$ denote the braid group on $n$ strands. The group…

Uniqueness conjecture. The statement of Theorem $$ holds for all finite-dimensional algebras.

Root-type orbit conjecture. Let $E_1,E_2\in\mathcal{E}$. Assume that there are $g_1,g_2\in B_{n-1}$ such that $g_1E_1$ and $g_2E_2$ have tame type but different root types. Then…