4 problems

Let $G$ be a simply-laced algebraic group, and let the cluster subalgebra constructed by Leclerc from modules of the preprojective algebra be a subalgebra of the coordinate ring of…

Let $\mathring{\mathcal{B}}_{v,w}$ be an open Richardson variety in a symmetrizable Kac--Moody setting, and let $\mathbb{C}[\mathring{\mathcal{B}}_{v,w}]$ carry the natural upper c…

Let $W$ be the Weyl group of a Dynkin diagram, and let $w,v,u\in W$ satisfy … Let $\mathscr{C}_{w,v}$ be the subcategory associated with $w$ and $v$, let $K_q(\mathscr{C}_{w,v})$ d…

Fundamental-group conjecture. For every $v\in W$,