7 problems

Let $M$ be a fixed closed hyperbolic $3$-manifold, and let $M_n$ be covers of $M$ that Benjamini–Schramm converge to hyperbolic $3$-space $\mathbb{H}^3$. The analytic torsion conve…

Let $\bm{G}_{g,L}$ be the random trivalent unicellular metric map of genus $g$ with boundary length $L$, and let $\bm{T}$ be the random infinite trivalent metric tree with independ…

Let $M$ be a compact $d$-dimensional manifold. An invariant random function $F$ is a Wigner wave for $M$ if there exists a sequence of $L^2$-normalized eigenvectors…

Let $X$ be the universal symmetric space and let $(M_n=\Gamma_n\backslash X)$ be a uniformly discrete expander family that BS-converges toward $X$. Fix an eigenvalue $\lambda_0$ of…

Let $G$) be a semisimple Lie group with trivial center, and let $(\Gamma_i)_{i\in\mathbb N}$ be a sequence of arithmetic lattices satisfying:…

Maximal surface-graph conjecture. The sequence $G_n$ Benjamini--Schramm converges, and its limit coincides with the UIPT.

Minor-exclusion Benjamini--Schramm conjecture. The sequence $G_n$ Benjamini--Schramm converges.