From Celestial Mechanics to Fluid Dynamics: Contact structures with singularities

Taking as starting point several examples from Celestial mechanics where regularization techniques bring singularities in, we will introduce the geometry of contact structures where the regularity of the contact 1-form is relaxed. Contact structures also show up modelling problems in Fluid Dynamics and singularities also appear naturally in this context (ongoing joint work with Robert Cardona and Daniel Peralta-Salas).  

Two main geometrical problems will be addressed in this talk: The existence problem of contact structures with singularities on a given manifold and the study of its Reeb Dynamics, in particular, the existence of periodic orbits (Weinstein conjecture).

This is joint work with Cédric Oms.

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