5 problems

Let ${\mathcal T}_\Lambda$ be the graph whose vertices are the basic maximal rigid $\Lambda$-modules, with edges given by mutation. Let ${\mathcal T}_\Lambda^\circ$ be the connecte…

Let $\mathcal B$ and $\mathcal S$ be the canonical and semicanonical bases, let $b_{\mathcal O}\in\mathcal B$ correspond to an orbit $\mathcal O$, and let $f_Z\in\mathcal S$ be ind…

Let $I'=I\setminus\{p\}$ index the irreducible components $Y_k$ of the exceptional variety $\mathfrak{L}=\mathfrak{L}_m$, and let $\widetilde E_k(m)$ be the characteristic function…

Let $Z$ be an irreducible component in the relevant module variety, and let $f_Z$ denote the corresponding semicanonical basis element. Lusztig's support conjecture. The semicanoni…

Let $C$ be a symmetric generalized Cartan matrix, let $\mathfrak{g}=\mathfrak{n}_-\oplus\mathfrak{h}\oplus\mathfrak{n}$ be its associated Lie algebra, and let ${\mathcal S}^*$ be t…