4 problems

Let $d=2$. A weight vector is a vector $\mathbf{w}=(w_1,w_2)\in\mathbb{R}^2$ with $w_i\geq 0$ and $w_1+w_2=1$. For a weight vector $\mathbf{w}$, let … where $|\cdot|_{\mathbb{Z}}$…

HAW conjecture. For any $x\in X$, the set $E^+(x,\infty)$ is hyperplane absolute winning (HAW) on $\mathbf{P}^+(\mathfrak{g})$. This is the homogeneous-space counterpart of the pre…

Let $\mathbf{w}=(w_1,\ldots,w_d)\in\mathbb{R}^d$ be a weight vector, meaning that $w_i\geq 0$ for $1\leq i\leq d$ and $\sum_{i=1}^d w_i=1$. Define … where $|\cdot|_{\mathbb{Z}}$ de…

Let $G$ be a Lie group, let $\Gamma$ be a lattice in $G$, and let $F^{+}$ be an $\operatorname{Ad}$-diagonalizable subsemigroup of $G$. Define … Here, a subset is hyperplane absolu…