Abstract: The first order partial differential equations are closely
connected to the underlying characteristic ODEs. The second order elliptic
and parabolic equations are as closely connected to the Brownian motion
and more general diffusions with a drift. From a variety of points of
view, the drift does not really matter - all duffusions look more or less
similar. As a caveat to this reasonable line of thought, I will describe
a menagerie of problems: linear and nonlinear, steady and time-dependent,
compressible and incompressible, where the drift and diffusion
confirm the Mayakovsky thesis "Woe to one alone!" Together, they
lead to enhanced mixing and improved regularity that are impossible for
each one of them to attain. Illustrations range from combustion to
coral reproduction.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006