6 problems

Let $G$ be a connected complex semisimple affine algebraic group with Lie algebra $\mathfrak{g}$. Let $(e,h,f)\in\mathfrak{g}^{\times 3}$ be a principal $\mathfrak{sl}_2$-triple, a…

Non-realizability conjecture. The closure $\overline{\mathcal{O}}_\textrm{min}^{E_6}$ is not isomorphic to any Hamiltonian reduction of the cotangent space $T^*V$ of a representati…

Let $\lambda=(\lambda_1,\dots,\lambda_n)\vdash N$, let $a$ be the unique integer with $\lambda_{a-1}=1$ and $\lambda_a>1$, and define … Set $m=\lambda_1+\dots+\lambda_a$, let…

Let $\mathcal{A}//\mathcal{P}$ denote the space of parabolic connections with its infinitesimal higher-diffeomorphism action, and let $\operatorname{Symp}_0$ denote the correspondi…

The cotangent bundle T^*\bm\hat{\mathcal{T}}^n is obtained by Hamiltonian reduction from the hyperkähler punctual Hilbert scheme, with its given symplectic structure near the zer…

Let $e_1,e_2\in\mathfrak{g}$ be nilpotent elements, and let $\mathfrak{m}_1,\mathfrak{m}_2\subseteq\mathfrak{g}$ be the subalgebras constructed for a covering pair of nilpotent orb…