A generalisation of the Cauchy-Kovalevskaia theorem

I prove, under mild assumptions, that solutions to linear evolution equations admit sectorial solutions. The size of the sector depends on the regularity of the initial data. If it is regular enough the solution is holomorphic and unique otherwise itis sectorial. I also prove that the result is optimal for many partial differential systems (which includes KdV and other examples).

Classical and quantum integrability

We give a sufficient condition for quantising integrable systems.

Analytic geometry and semi-classical analysis

Expository paper on the relations between perturbation theory of pseudo-differential operators, finiteness theorems and deformations of Lagrangian varieties.