| Abstract: |
| In this talk I report on joint work with Patrick G\`erard and Petar Topalov concerning the construction of global Birkhoff coordinates for the Benjamin-Ono (BO) equation on the torus. In these coordinates, the BO 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. As an application, we obtain sharp well-posedness results for the Benjamin-Ono equation in Sobolev spaces of low regularity. |
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