Stellar population synthesis as an inverse problem. Application to nearby galaxies.

The problem of ``stellar population synthesis'' is to derive the stellar population of an unresolved stellar system using a database of stars or clusters. In this talk I will set out the two different approaches adopted since the 60s in order to solve this problem and will discuss the connected drawbacks. Then I will expose an inverse stellar population synthesis method that I developped with Didier Pelat from the ``Observatoire de Meudon'' (France). This method provides a full knowledge of all possible exact solutions and deals with the minimisation problem when an approached solution is required. In addition, it allows to compute the uncertainties around the solutions and provides a criterium to sort the various solutions by order of merit. After introducing astrophysical constraints while searching for a solution, we found that these have little effect on the results. The method and the analysis have been applied to the central regions of a sample of 10 active and 2 normal galaxies in order to gain new insight into the starburst-AGN connection.