5 problems

Bijectivity conjecture. The map $\pi\colon\operatorname{silt}\nolimits^{\mathcal F}{\mathcal T}\to{\it d}\strut\kern-.2em\operatorname{-ctilt}\nolimits{\mathcal C}$ is bijective fo…

Let $A$ be a finite-dimensional algebra over a field $K$. Write $K_0(\operatorname{\mathsf{proj}} A)$ for the Grothendieck group of finitely generated projective $A$-modules, and l…

Silting mutation conjecture. Then $T$ is tilting and $\operatorname{End}_A(T)$ is a $d$-representation infinite algebra.

Let $k$ be a field, let $A$ be a finite-dimensional $k$-algebra, and let $n$ be the number of pairwise non-isomorphic simple $A$-modules. Let $\mathsf{D}^{\rm b}(\mathsf{mod} A)$ b…

Let $k$ be a field, let $A$ be a finite-dimensional $k$-algebra, and let $\mathsf{D}^{\rm b}(\mathsf{mod} A)$ be its bounded derived category. An object is presilting if it has no…