## – Europe/Lisbon — Online

Robert Berman, Chalmers University of Technology

Kähler-Einstein metrics, Archimedean Zeta functions and phase transitions

While the existence of a unique Kähler-Einstein metrics on a canonically polarized manifold $X$ was established already in the seventies there are very few explicit formulas available (even in the case of complex curves!). In this talk I will give a non-technical introduction to a probabilistic approach to Kähler-Einstein metrics, which, in particular, yields canonical approximations of the Kähler-Einstein metric on $X$. The approximating metrics in question are expressed as explicit period integrals and the conjectural extension to the case of a Fano variety leads to some intriguing connections with Zeta functions and the theory of phase transitions in statistical mechanics.

### Video

### Additional file

Projecto FCT `UIDB/04459/2020`.