The real Monge-Ampère equation on the boundary of a simplex, and the SYZ conjecture

par Mattias Jonsson (University of Michigan)

jeudi 18 janv. 2024, 10:30 → 12:30 Europe/Paris

The SYZ conjecture concerns the geometry of the fibers of a degenerating family of complex Calabi--Yau manifolds. Recent deep work by Yang Li reduces this to a conjecture in non-Archimedean geometry. I will report on joint work with Hultgren, Mazzon, and McCleerey where we prove the latter conjecture in a particular case. The key step in our approach is to solve a real Monge-Ampère equation on the boundary of a simplex.