9 problems

Let $G$ be a reductive group over a local field, let $\mu\in X_*(T)_+$ be a dominant cocharacter, and let $\tau$ represent the unique basic $\sigma$-conjugacy class such that…

Nestedness Conjecture. The stratification is nested: there is a partial order on the index set $\{\alpha\}$ such that

Let $X$ be a reduced scheme of finite type over a field $k$ of characteristic $0$, and let $x\in X$ be a closed point. The ridge invariant of $X$ at $x$ is … Here $C_x(X)$ is the t…

Orbit-stratification conjecture. There exists a finite partially ordered set $(X,<)$ describing the $L^+G$-orbits in $\widetilde{\operatorname{Gr}}_{\mu_{\bullet}}$. Equivalently,…

Tame tangles approximate transversal tangles. Any compact framed transversal $m$-tangle can be approximated by compact tame $m$-tangles.

Tame diagrams approximate all diagrams. Every compact framed conical stratification $(\bI^n,f)$ has an arbitrarily close approximation by a compact manifold $n$-diagram.

Let the de Rham moduli space $\mathbb{M}_{\mathrm{dR}}(X,r)$ be equipped with its oper stratification, whose strata are indexed by $\alpha$. Oper Stratum Conjecture. The oper strat…

Let $M$ be a (quasi-)projective variety with a stratification by locally closed subsets … The stratification is nested if there is a partial order $(\Lambda,\leq)$ such that … For…

Nested-stratification conjecture. The stratifications of $M_{\rm DR}(X,r)$ and $M_{\rm H}(X,r)$ are nested, and their strata have the same arrangement under the stated identificati…