Geometry & Topology

The talk aims to explain the orbifold regularity problem for canonical Kähler metrics on singular spaces. I will begin with a brief overview of canonical Kähler metrics and the Calabi problem, focusing more on the Kähler–Einstein setting. I will then discuss how singular Kähler–Einstein metrics are defined and what kind of singular spaces interest us. Finally, I will present the orbifold regularity problem of canonical Kähler metrics and explain the idea and strategy for solving the Kähler Calabi–Yau case. This talk is based on joint work with Henri Guenancia and Mihai Păun.