6 problems

Intersection-cohomology stalk conjecture. Its stalk at $(\phi,\underline{c},\underline{s})$ is isomorphic to

Normality conjecture. The scheme $\fM^\alpha(A)$ is normal; consequently, it is the normalization of $\bM^\alpha(A)$.

Let $|1^d\rangle=[\mathcal U_G^d]$ be the fundamental class in equivariant intersection cohomology, and let $\widetilde W^{(\kappa)}_n$ denote the positive modes of the generators…

Let $\cal G$ be an affine Lie algebra with connected Dynkin diagram, let $\cal G^{\vee}$ be its Langlands dual, and let $G_{\cal G^{\vee}}$ be the semisimple simply connected group…

Central-fiber repellent conjecture. The central fiber inside the intermediate open subspace coincides with the repellent:

Let $G$ be a reductive group, and let $\varpi:\CU_{G,\mu}^{\lambda^{(1)},\ldots,\lambda^{(n)}}(S_{k_1,\ldots,k_n})\to\CU_{G,\mu}^{\lambda}(S_k)$ be the proper birational morphism c…