Emergent complex geometry

  • Robert J. Berman

    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Göteborg, Sweden
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This is a double exposure of the probabilistic construction of Kähler–Einstein metrics on a complex projective algebraic variety – where the Kähler–Einstein metric emerges from a canonical random point process on – 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 (with respect to the trivial absolute value) also emerges from the probabilistic framework.