We want to understand spaces that parameterize projective subvarieties. One way to do this is to look at Algebraic Cycles. An Algebraic Cycle is a formal sum of irreducible closed subvarieties. If we take a family of irreducible subvarieties, its limit may have several irreducible components, i.e. the limit may be a general sycle.
We want to study this phenomenon and the Chow Varietes are a way of doing thins. Simply put, the points of a Chow variety are Algebraic Cycles. We will explain at the Chow - Van der Waerden Theorem that imbeds the variety into projective space. Finally we move on to a specific example, 0-cycles. We can use symmetric polynomials to work with 0-cycles. Using this we will look at the tangent space, and derive a formula for the tangent space of a multiple of smooth point.

Basic facts about proper forcing will be presented.

In this talk I will present some recent results concerning the
asymptotic self-similar patterns of degenerate diffusion in an infinite
porous medium with vanishing at infinity variable density.

The asymptotic pattern turns out to strongly depend on the decay rate of
the density. For "slowly" decaying densities, the picture is similar to
the homogeneous case (Barenblatt-type solutions), whereas for densities,
decaying fast enough, a completely different behavior, typical of problems
in bounded domains, arises.

For intermediate decay rates, both descriptions are correct, providing an
example of matched asymptotics.