6 problems

Let $G$ be the reductive group, let $b\in G(\breve{F})$ and let $\mu$ be a cocharacter, with associated affine Deligne–Lusztig variety $X^{\mathcal{K}_p}_\mu(b)$. Write…

Zhou's conjecture. If $(\lambda,b)$ is Hodge–Newton irreducible, then $\eta_G$ induces a bijection

A monotone affine vector variational inequality (AVVI) has $m$ criteria when its vector-valued objective has $m$ components, and its solution set may have several connected compone…

Assume that $G_{\mathrm{der}}$ is simply connected. Let $D=G_{\mathrm{ab}}=G/G_{\mathrm{der}}$ be the maximal abelian quotient of $G$, and let $\delta:G\rightarrow D$ be the projec…

Let $(\widetilde{G^*},A^*,G^*)$ be in Situation $(0)$, and let $B$ be the parameter set used to define the connected components. Suppose … Let $H$ be a $B$-invariant subgroup of…

Connected-component inclusion conjecture. Then