4 problems

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:…

Fix an arithmetic planar lattice $\Omega$, and define its zeta-function of well-rounded sublattices by … The abscissa of convergence is the value of $\rho$ such that the Dirichlet…

The cohomological spectrum conjecture. The lattices $\Gamma_{K_1}$ and $\Gamma_{K_2}$ are $L$-equivalent in $G_{1,\infty}\simeq G_{2,\infty}$.

The arithmetic-to-spectrum conjecture. The lattices $\Gamma_{K_1}$ and $\Gamma_{K_2}$ are $L$-equivalent in $G_{1,\infty}\simeq G_{2,\infty}$.