Let (M, g) be Riemannian four-manifold. Does there exist a
non-zero function f:M->R such that
(*) f^2 g is flat?
(**) f^2 g satisfies Einstein equations?
Most people know the answer to (*). Nobody (really) knows the full
answer to (**). In this talk I will provide the answer to
(***) f^2 g is Kahler for some Kahler form?

In this talk we will discuss various aniosotropic PDEs. We will then discuss integro-differential
equations inspired from (BV, L2) and (BV, L1) decompositions. Although the original motivation came from a variational approach, the resulting IDEs can be extended using standard techniques from PDE-based image processing. We use filtering, edge preserving and tangential smoothing to yield a family of modified IDE models with
applications to image denoising and image deblurring problems.

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and Gaussian distributions for various functionals of the process.