4 problems

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…

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.

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…