8 problems

Let $G$ and $G'$ be groups with Cayley graphs whose asymptotic cones are isometric. A group is non-elementary hyperbolic if it is hyperbolic and is not virtually cyclic. Sapir's co…

Volume growth and asymptotic cone dimension conjecture. (1) If

Fix a polystable negative valuation $v$ on $X$. Let $\mathcal M_v$ be the space of compatible Calabi–Yau metrics on $X$ with $v=v_\omega$, let $\mathcal C_v$ be the corresponding w…

Let $X$ be a complete Calabi–Yau manifold in the setting of Theorem … should hold without the quadratic curvature decay assumption. This is the expected extension of the paper's ma…

Restrict to the free group $G=F(A)$, let $\Theta\subseteq P(G)$ be a set of cyclically reduced representatives for the equivalence classes in $P(G)$, and let $\tau$ be the stable n…

Let $G$ be a group with norm $\|\cdot\|$, and let $F(G)$ denote the free group on the underlying set of $G$, with generators written $\overline g$. For $g_1,\dots,g_n\in G$, compar…

Let $G$ be a group equipped with the bi-invariant metric norm $\\|\cdot\\|$. For elements $g_1,\dots,g_n\in G$, consider the sequence of normalized norms of products of equal power…

A graph is called $\delta$-CAT(0) when its geodesic triangles satisfy the corresponding CAT(0) comparison condition up to an additive constant, and it is asymptotically CAT(0) when…