Point Set Objects: Geometry, Dynamics and Applications.

In this talk we deal with point set objects.The representation of point
set objects is done by using implicit surface techniques with topological
guarantees. Implicit surfaces and machine learning techniques can be put
together to understand 3D reconstruction of oil reservoir from seismic
data. Topology and geometry problems will be pointed out.

We also show how to model the dynamics of point set objects by combining
lagrangian fluid representation with non-newtonian dynamics and
hodge-helmholtz decomposition to model multiphase flow. Geometry an
numerical problems are indicated. Also we will point out an application
in turbidite geological formation.