Finiteness of totally geodesic exceptional divisors in Hermitian locally symmetric spaces
(Joint work with J. Maubon). I will prove that on a smooth
complex surface which is a compact quotient of the bidisc or of the 2-ball, there is at most a
finite number of totally geodesic curves with negative self intersection. More generally, there are
only finitely many exceptional totally geodesic divisors in a compact Hermitian
locally symmetric space of the noncompact type of dimension at least 2.
This will be deduced from a convergence result for currents of integration along totally geodesic
subvarieties in compact Hermitian locally symmetric spaces which itself follows from
an equidistribution theorem for totally geodesic submanifolds in a locally symmetric
space of finite volume.