Mattew Stover

  I will describe joint work with Domingo Toledo that studies residual
finiteness (RF) for central extensions of lattices in PU(n,1). There are
two motivations for this. First, RF for lattices in the universal cover
of PU(n,1) ends up being a key case for understanding RF for lattices in
nonlinear Lie groups (modulo a major, widely believed conjecture).
Second, our main application is the construction of n-dimensional
negatively curved smooth projective varieties for all n > 1 that do not
admit a locally symmetric metric, building on work of Mostow-Siu and
Zheng (n=2) and Deraux (n=3).