Which consistent statements can be forced to be true?
It is shown that "resectionable" \Sigma_1 statements about parameters
in H_{\omega_2} which are "honestly consistent" can be forced
to be true in a stationary set preserving extension, and we also show
that a strong form of BMM, according to which all "honestly consistent"
\Sigma_1 statements about parameters in H_{\omega_2} are true,
is consistent. We also give some applications.

Finding a point on a variety amounts to finding a solution to a system of
polynomials. Finding a "rational point" on a variety amounts to finding a
solution with coordinates in a fixed base field. (Warning: our base field
will not be the field of rational numbers Q.) We will present some
theorems about when it is possible to find such a rational point. We will
state Tsen's theorem and the Chevalley-Warning Theorem. We will also
state some more recent results of Hassett-Tschinkel and
Graber-Harris-Starr, which rely on the notion of a "rationally connected
variety". This notion is an analogue of the notion of "path
connectedness" in topology.

We give recent results about the global well-posedness of the stochastic primitive equations in 2D and 3D.