Mattias Jonsson: On the Yau–Tian–Donaldson conjecture

Location

FR4, Albanova

Schedule

14:15–15:00 Pre-colloquium by Edoardo Mason  in FB54.

15:15–16:15 Colloquium lecture by Mattias Jonsson.
16:15–17:00 SMC social get together with refreshments.

Abstract

Any compact Riemann surface is topologically determined by its genus, i.e., the number of “holes”, and by the Uniformization Theorem it admits a unique metric of constant curvature \(1\), \(0\) or \(-1\). In higher (complex) dimension, the situation is more complicated, but the Yau–Tian–Donaldson conjecture states that the existence of a metric of constant scalar curvature—which is an analytic object—is governed by a purely algebro-geometric condition. I will present joint work with S. Boucksom, where we prove a version of this conjecture.