Emergent complex geometry (Q6200240)

Summary: This is a double exposure of the probabilistic construction of Kähler-Einstein metrics on a complex projective algebraic variety \(X\) -- where the Kähler-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. For the entire collection see [Zbl 07816358].