TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Summer Semester 2023)

Mattias Jonsson (University of Michigan)

Abstract:

A celebrated result of Yau says that every compact Kähler manifold with trivial canonical bundle admits a Ricci flat metric in any given Kähler class. The proof amounts to solving a complex Monge-Ampère equation. I will discuss joint work with Hultgren, Mazzon, and McCleerey, where we solve a “tropical” Monge–Ampère equation, on the boundary of simplex. Through recent work of Yang Li, this has applications to the SYZ conjecture, on degenerations of Calabi-Yau manifolds.