9 problems

Let $D_n$ be the cohomology algebra of the configuration spaces of $n$ ordered points in $SU_2$ up to translations, and let $M_n$ be the intersection cohomology ring of the hyperto…

Let $H$ be a unimodular hyperplane arrangement with corresponding affine hypertoric variety $\mathfrak{M}$ and underlying matroid $M$. Let $S_k(M)$ be the extended matroidal Schur…

Projective resolutions of standard modules are interpreted using certain Heegaard diagrams. Holomorphic-disk conjecture. Holomorphic disk counts in these diagrams should encode bot…

Let $\mathcal{V}$ be a polarized arrangement, not necessarily rational, with associated affine complexification $(V+\eta)_{\mathbb{C}}$ and complexified hyperplane arrangement…

Let $\mathcal{V}$ be a polarized real arrangement, let $\mathcal{X}_{\mathcal{V}}$ be its complexified hyperplane complement, and let $\widetilde{B}(\mathcal{V})$ be the universal…

Let $\mathcal{X}=[X/T]$ be a smooth Deligne–Mumford quotient stack, where $X$ is a smooth scheme over a field $k$ and the torus $T$ acts with finite stabilizer. Let $\mathbf{M}$ an…

Let $G$ be a group with maximal torus $T$ and Weyl group $W$, and let $\mathfrak{M}_{\alpha,0}(G)$ and $\mathfrak{M}_{\alpha,0}(T)$ be the corresponding symplectic quotients. Assum…

Let $G$ be a group with maximal torus $T$, Weyl group $W=N(T)/T$, and associated symplectic quotients $\mathfrak{M}_{\alpha,0}(G)$ and $\mathfrak{M}_{\alpha,0}(T)$. Let $\Phi_0(G)$…

A symplectic algebraic variety is a connected algebraic variety equipped with a symplectic structure. Let $T^d$ be an algebraic torus of dimension $d$ acting effectively and hamilt…