7 jul 2026   [open in google calendar]

Centro de Giorgi, Sala Conferenze

Abstract.

The Allen–Cahn model for phase transitions is one of the most extensively studied PDEs in geometric analysis, largely because its solutions can approximate minimal hypersurfaces through their level sets. This perspective has led to remarkable results in the closed setting. However, the classical framework is not well suited to boundary value problems such as the Plateau problem, since a non-separating hypersurface cannot, in general, arise as the regular level set of a real-valued function. Instead, we study an Allen–Cahn equation for sections of a suitable line bundle, which removes this obstruction but introduces new geometric and analytical challenges to the classical Allen–Cahn framework.