More than 65 years ago, John Wheeler suggested that quantum uncertainties of the metric
would be of order one at the Planck scale, leading to large fluctuations in spacetime …

Let Γ be a lattice in SO_0(n,1). We prove that if the associated locally symmetric space
contains infinitely many maximal totally geodesic subspaces of dimension at least 2, then Γ …

For n≥ 2, we prove that a finite volume complex hyperbolic n-manifold containing infinitely
many maximal properly immersed totally geodesic submanifolds of real dimension at least …

Homology and homotopy complexity in negative curvature Page 1 DOI 10.4171/JEMS/971 J.
Eur. Math. Soc. 22, 2537–2571 c European Mathematical Society 2020 Uri Bader · Tsachik …

We exhibit closed hyperbolic manifolds with arbitrarily small systole in each dimension that
are not quasi-arithmetic in the sense of Vinberg, and are thus not commensurable to those …

We show that large classes of non-arithmetic hyperbolic n-manifolds, including the hybrids
introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only …

arXiv:1512.03661v2 [math.GT] 30 Dec 2015 Page 1 HYPERBOLIC FOUR-MANIFOLDS
BRUNO MARTELLI Abstract. This is a short survey on finite-volume hyperbolic four-manifolds …

In the 1st paper of this series we studied the asymptotic behavior of Betti numbers, twisted
torsion, and other spectral invariants for sequences of lattices in Lie groups G. A key element …

The purpose of this article is to produce effective versions of some rigidity results in algebra
and geometry. On the geometric side, we focus on the spectrum of primitive geodesic …

This essay points to many of the interesting ramifications of Margulis' arithmeticity theorem,
the superrigidity theorem, and normal subgroup theorem. We provide some history and …