Asteroseismology's new constraints on stellar models and Galactic Archaeology: Where are we now and where are we going?

After a short introduction describing the whys and wherefores of the recent and growing interaction between Milky Way physicists, stellar evolution physicists, chemical abundances physicists, and asteroseismologists, which forms the ground of this workshop, we address some important points affecting the levels of accuracy on global stellar parameters, such as mass, radius, and age, which were raised during the final discussion of the workshop. We recall how asteroseismic parameters, especially when coupled with spectroscopy and photometry, greatly help to reduce uncertainties. We show how poorly known physical aspects, such as diffusion, rotation, and outer physical conditions, must however be kept in mind when assessing these uncertainties. We then summarise the huge advance in terms of spectroscopic follow-up of seismic targets that took place in the last couple of years opening the doors for the first results in Galactic Archaeology making use of seismic distances, masses, radii, and ages. We conclude by presenting two tables: (1) an update of the table of uncertainties built at the Sesto workshop in 2013, and (2) a similar table with what should be reached for Galactic Archaeology purposes.