11 problems

Let $A$ be an alcove in the space of real stabilities, and let $\mathcal{E}(A)$ be the set of joint eigenlines for quantum multiplication by equivariant cohomology classes of $Y$ o…

Generic t-structure conjecture for the Koszul-dual algebra. The function $\pi$ defines a $t$-structure on the derived category of differential graded modules over

Generic perverse-equivalence conjecture for principal blocks. There is a perverse equivalence between $kD\rtimes E$ and $kGb$ with perversity function $\pi$.

Chuang–Rouquier perversity conjecture. The derived equivalence should be perverse, with a non-decreasing perversity function for that order.

Let $G$ be a finite group of Lie type in characteristic $r\ne p$, let $P$ be an abelian defect group, let $A$ be a $P$-block of $kG$, and let $B$ be its Brauer correspondent in…

Let $\ell$ be a prime and let $G=\mathbb{G}(q)$ be a finite group of Lie type, where $p\ne\ell$ and $q$ is a power of $p$. Let $D\in\operatorname{Syl}_{\ell}(G)$, let…

Let $C$ be the cohomology complex associated with the relevant Deligne–Lusztig variety, and let $\mathcal{S}_{B_0(H)}$ denote the simple-module indexing set for the local principal…

Let $G$ be a finite group of Lie type, let $B_0(G)$ be its principal block, and let $Y_{\kappa/d}$ be the relevant Deligne–Lusztig variety. For a unipotent character $\chi$ of $KG$…

Let $B$ be a unipotent block of $kG$ with cyclic defect groups, and let $B'$ be its Brauer correspondent. Let $\pi_{\kappa/d}$ be the perversity function defined from the generic d…

Let $\chi_1,\dots,\chi_s$ be the unipotent ordinary characters in a unipotent $\ell$-block $B$ of $kG$ with abelian defect group. Let $B'$ be the Brauer correspondent of $B$, and l…

Let $G=\b G^F$ be a finite group of Lie type, let $B$ be a unipotent $\ell$-block with abelian defect group, and let $b$ be its Brauer correspondent. Let $\chi_1,\dots,\chi_s$ be t…