In the previous talks we have seen that in certain problems in complex analysis, one can try to first construct a smooth $($not analytic$)$ solution to the initial problem with the required properties, which is is in general a rather easy task. In a second step one tries to correct the solution to make it holomorphic maintaining the main properties of the problem: if $f$ is a smooth solution to the initial problem and if $u$ is a suitable solution to ${\overline{\partial}}\,$ $u=g$ where $g={\overline{\partial}\,}$ $f$, then $F=f-u$ satisfies ${\overline{\partial}\,}$$F=0$ so that $F$ is analytic. The challenge here is that the correction u does not destroy the properties required by the initial problem $($for instance values in given points, norms, etc.$)$. We have seen different types of problems where this
scheme produces solution $($e.g. interpolation problems, corona/Bézout-type problems, Cousin problem$)$.

A central tool is Hörmander's theorem which gives the existence of d-bar solutions with norm estimates in suitable weighted spaces, the weight involving subharmonic functions.

The aim of this last talk is to solve an interpolation problem in the Fock space $($which is the space of entire functions square integrable with respect to a gaussian weight$)$. More precisely, we will show how a certain density condition allows to construct the subharmonic function required by Hörmander's theorem.