In this talk I report on joint work with Patrick Gérard concerning the construction of global
Birkhoff coordinates for the Benjamin-Ono equation. In these coordinates this equation can
be solved by quadrature, meaning that it is an integrable (pseudo)differential equation in
the strongest possible sense.  The construction is based on the Lax pair formulation
of this equation. I will present spectral properties of the Lax operator, discuss a generating
function of the Benjamin-Ono hierarchy, which allows to establish various trace formulas,
and introduce the Birkhoff coordinates. Furthermore, I will provide a characterization of
finite gap solutions.

海报