## Séminaire de Géométrie et Quantification |

**Alexandre
Odesski**

(Brock
University et IHES)

*Integrable
structures of dispersionless systems and differential geometry*

Lundi 15 mai à 15h30, salle 201, IHP

Résumé : We obtain variational formulas
for holomorphic objects on Riemann surfaces with respect to arbitrary
local coordinates on the moduli space of complex structures. These
formulas are written in terms of a certain differential geometric
structure on the moduli space which corresponds to the pairing
between the space of quadratic differentials and the tangent space to
the moduli space. This canonical object satisfies certain commutation
relations which appear to be the same as the ones that emerged in the
integrability theory of Whitham type hierarchies. Driven by this
observation, we develop the theory of Whitham type hierarchies
integrable by hydrodynamic reductions as a theory of certain
differential-geometric objects.