8 problems

Let $\mathcal{H}_0(r,d)$ be the locus of Higgs bundles $(\bar{\partial}_E,\theta)$ in $\mathcal{H}(r,d)$ satisfying … Let $\mathcal{F}$ be the fibre space over $\mathcal{H}_0(r,d)$…

Let $\CN^L\subset\fg^L$ be the nilpotent cone, and let $\fn_-^L$ be the negative nilpotent subalgebra. The geometric action of $\fg^L$ is defined on … The local cohomology module i…

Let $\check{G}$ be a pinned connected reductive algebraic group over an algebraically closed field $k$ of characteristic zero, let $G$ be its Langlands dual group, and let…

The filtration–singular-support conjecture.

Let the nilpotent cone be decomposed into components of type $(1,2)$ for rank $3$ Higgs bundles. A component is called very stable if it contains a very stable Higgs bundle. Very-s…

Nilpotent-cone domination conjecture. The energy density satisfies

Let $X$ be a smooth complex projective curve, let $G=GL_n$, and let $\mathcal N_{X,G}\subset T^*Bun_G(X)$ be the global nilpotent cone. A cuspidal Hecke eigensheaf is an automorphi…

Let $G$) be a simply connected semisimple algebraic group over an algebraically closed field of good characteristic, and let $\mathcal{N}$ denote the nilpotent variety in the Lie a…