Emergent complex geometry

Abstract

This is a double exposure of the probabilistic construction of Kahler-Einstein metrics on a complex projective algebraic variety X - where the Kahler-Einstein metric emerges from a canonical random point process on X - and the variational approach to the Yau-Tian-Donaldson conjecture, highlighting their connections. The final section is a report on joint work in progress with Sébastien Boucksom and Mattias Jonsson on how the non-Archimedean geometry of X (with respect to the trivial absolute value) also emerges from the probabilistic framework.

To appear in the proceedings of the ICM 2022

References in corpus (2)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• K-stability of constant scalar curvature Kähler manifolds