Betti numbers of real semi-stable degenerations via real logarithmic geometry

In a joint work with Emiliano Ambrosi, we study the real topology of totally real semistable degenerations, with certain technical conditions on the special fiber X0, and we give a bound for the individual real Betti numbers of a smooth fiber near 0 in terms of the complex geometry of X0. The main ingredient is the use of real logarithmic geometry, which allows to work with degenerations which are not necessarily toric and hence to go beyond the case of tropically smooth degenerations. This, in particular, generalizes previous work of Renaudineau-Shaw, obtained via tropical techniques, to a more general setting.