A broad effort is ongoing with large spectroscopic surveys such as APOGEE, Gaia-ESO, GALAH, LAMOST from which stellar parameters, radial velocities and detailed chemical abundances can be measured for CoRoT, Kepler, and K2 targets. In addition, asteroseismic data of red-giants stars observed by the space missions CoRoT and Kepler allow determination of stellar masses, radii, and can be used to determine the position and ages of stars. This association between spectroscopic and asteroseismic constraints provide a new way to understand Galactic and stellar evolutions.

To exploit all potential of this combination it would be crucial to develop our approach of synthetic populations. We develop the Besançon Galactic model for which stellar evolution predictions providing the global and asteroseismic properties, as well as the surface chemical abundances along the evolution of low- and intermediate-mass stars are included. For the first time, the BGM can explore the effects of an extra-mixing occurring in red-giant stars. These synthetic populations can be compare with the significant large surveys as APOKASC (APOGEE -Kepler) or CoRoGES (CoRoT-GES).

I will present the evolution of red-giant stars, computed with the stellar evolution code STAREVOL including the effects of thermohaline mixing together with rotational mixing on the surface chemical abundances as well as on the Galactic chemical evolution of helium-3. I will also present the first comparison between synthetic populations computed with the Besançon Galaxy model and the last release of the Gaia-ESO survey, exploring the efficiency of extra mixing with the stellar metallicity, mass, and age (Lagarde et al. 2019).

We emphasize the usefulness of population synthesis tools to test stellar models and transport processes inside stars. We show that transport processes occurring in red-giant stars should be taken into account in the determination of ages for future Galactic archaeology studies.