3 problems

Let $S$ be a finitely generated graded $\Bbbk$-algebra that is Koszul, and let $T^i_{S/\Bbbk}$ denote its $i$th cotangent cohomology, with its internal grading. The extremal-weight…

Let $\mathcal{K}$ be a flag complex, let $\mathbf{a},\mathbf{b}\in\mathbb{Z}_{\geq 0}^{\mathcal{V}}$ have disjoint supports, and write $|\mathbf{b}|$ for the sum of the entries of…

Let ${\mathcal{M}}$ be a matroid, and let $T^2({\mathcal{M}})$ denote its second cotangent cohomology module. The join of matroids is their join as simplicial complexes; a matroid…