There are many examples in mathematics, both pure and applied, in which
problems with symmetric formulations have non-symmetric solutions.
Sometimes this symmetry breaking is total, as in the example of
turbulence, but often the symmetry breaking is only partial. One technique
that can sometimes be used to constrain the symmetry breaking is
reflection positivity. It is a simple and useful concept that will be
explained in the talk, together with some examples. One of these concerns
the minimum eigenvalues of the Laplace operator on a distorted hexagonal
lattice. Another example that we will discuss is a functional inequality
due to Onofri.
The talk is based on joint work with E. Lieb.