The talk will be about two problems in the theory of Beurlingand Carleman classes of smooth functions.
The first one is to describe the image of a Beurling or Carleman class underBorel's map ( whichmaps infinitely differentiable functions  to the jets of their Taylorcoefficients at a given point). The second one is  how to construct a function inBeurling  or Carleman class with prescribed Taylor coefficients.
In the talk, I will present  solutions to both problems in some Beurlingand Carleman classes (both quasianalytic and non-quasianalytic).