Name: Ana Reguera

Title: Divisorial valuations dominating a normal surface singularity.

Abstract:
>From results by G{\"o}hner and Cutkosky it follows that a complete normal
local ring $R$ of dimension 2 has a rational singularity if and only if all
graded algebras $gr_\nu R$ defined by divisorial valuations $\nu$
dominating $R$ are noetherian. We will show a constructive way of proving
the noetherianness of $gr_\nu R$ when $R$ has a rational singularity, and
describe how to get a generating sequence for $\nu$. We will also study the
Hilbert function defined by $\nu$.