3 problems

Let $A$ be a properly stratified algebra with a simple preserving duality. Write $\fdim(A)$ for its finitistic dimension, $\fdim_{\Delta}(A)$ for its Delta-finitistic dimension, an…

Weighted-poset equivalence conjecture. The categories $\mathcal{S}(W,S,S)$ and $\mathcal{S}(W',S',S')$ are equivalent if and only if their weighted posets are isomorphic.

DPS conjecture. There is a faithful right ${\mathcal H}$-module $T^\dagger$, filtered by various $S_\omega$, such that the modules $\Delta(\omega)$, with $\omega\in\Omega$, form a…