3 problems

Draisma's conjecture. The affine infinite Grassmannian $\widetilde{\operatorname{Gr}}(\infty/2,V^*_\infty)$ is topologically $S_\infty$-noetherian: every descending chain of…

Let $C$ be an algebraically closed extension of infinite transcendence degree of an algebraically closed field $k$ of characteristic $0$, let $G$ be the group of automorphisms of…

Let $k$ be a field, let $K=k(\Psi)$ with its standard $\mathop{\mathfrak{S}}\nolimits_{\Psi}$-action, and let $K[\binom{\Psi}{s}]$ denote the smooth…