4 problems

Let $\mathsf{FO}^\phi(\#)$ be first-order logic with the Härtig quantifier, interpreted over finite structures, and let an extension of this logic be given. A limit law means that,…

Let $e\in\mathfrak{sp}_{2n}$ be a nilpotent element whose partition has five parts, and let $S_e$ be the set of centrally extended orbits generated by the good multiplication rules…

Let $e$ be a nilpotent element in a classical Lie algebra $\mathfrak{g}$, with partition $\lambda$, and let $\lambda^\intercal$ be its dual partition. Form $\lambda_{\mathrm{red}}$…

Let $(e,h,f)$ be an $\mathfrak{sl}_2$ triple in $\mathfrak{g}$, let $T_e$ be the torus with Lie algebra $\mathbb{C}h$, and let $\operatorname{Spr}$ be the Springer fiber. Set…