Conférencier: Freid Tong, University of Toronto

Calabi-Yau metrics are Ricci-flat and Kähler metrics and they are a central part of Kähler geometry. The construction of Calabi-Yau metrics on compact Kähler manifolds has been understood since Yau's resolution of the Calabi conjecture. By contrast, the situation in the complete non-compact case is much more intricate and remains an active area of research. In this talk, I will discuss some recent developments in the study of complete Calabi-Yau metrics where the regularity theory of an optimal transport problem plays a big role. This is based on joint work with Tristan Collins and Shing-Tung Yau.