Speaker:
Mohammad Moghaddam (IPM, Teheran, Iran)

Title:
The topological, metric and parametric structures on the space of
valuations centered on a ring

Abstract:
In algebraic geometry, the topological study of the space of valuations,
Riemann-Zariski manifold, began by the work of Zariski on local
uniformization problem. We show that the structure of this space can be
studied be the use of  two different representations of the valuations,
i.e., the key-polynomial and the generalized power series representation
of the valuations. These different descriptions allows us to study the
contact structure of the valuations on the Riemann-Zariski manifold and
to interpret the contact in terms of the truncations of generalized
power series. Moreover, it allows us to give a natural parametrization
of the Riemann-Zariski manifold.