6 problems

Let $T$ be a tree and let $\Phi:\mathcal{F}_T\to\mathcal{F}_T$ be an autoequivalence of Penner type. Let $\Phi_{\mathrm{Stab}}$ and $\Phi_{\mathbb{C}}$ be the induced actions on th…

Let $G$ be the group of autoequivalences of the category under consideration, and let the shifting numbers assign numerical invariants to elements of $G$. Fan–Filip's quasimorphism…

Let $Y$ be the surface, let $D\subset Y$ be the boundary divisor, let $U=Y\setminus D$, and let $Z$ be the union of all $(-2)$ curves in $Y$. Write $Z'=Z\cap U$, let $\bar{Q}$ be t…

Let $Y$ be the surface, let $D\subset Y$ be the boundary divisor, and put $U=Y\setminus D$. Let $\mathcal{A}'\subset\mathcal{A}$ be obtained by restricting to curves contained in…

Let $\mathcal C$ be a triangulated category for which the compactification $\overline M$ is defined, and let $\beta\colon\mathcal C\to\mathcal C$ be an auto-equivalence. Call…

Let $\mathcal{C}$ be a $2$-Calabi-Yau triangulated category with cluster structure, let $T$ be a cluster tilting object, and let $\phi$ be a cluster map sending cluster tilting obj…