A non-archimedean characterization of essential valuations of surfaces

I will present a criterion describing the essential valuations of a
normal surface singularity in terms of the analytic structure of its
non-archimedean link.  The latter, a non-archimedean version of the
classical link of a singularity, is a space of valuations carrying an
additional analytic structure, and I will describe it using tools from
Berkovich geometry.