Monge-Ampere Equations: Beyond the Classical Cases

Explore a mathematics colloquium lecture that delves into the generalization of Monge-Ampère equations beyond their traditional applications in real and complex analysis. Learn about recent developments in extending these equations to new mathematical contexts, including calibrated and quaternionic geometries. Discover groundbreaking research introducing an octonionic analogue of Kähler metrics on 16-manifolds and the corresponding octonionic version of the Monge-Ampère equation. Understand the proof of an octonionic Calabi-Yau type theorem and its implications, presented through collaborative research with P. Gordon. Gain insights into how these classical equations continue to evolve and find new applications in advanced geometric analysis.