A Survey on Generalized Monge-Ampère Equations and Subvarieties

Explore the mathematical foundations and applications of generalized Monge-Ampère equations in this comprehensive 56-minute conference talk from BIMSA's ICBS2025 series. Delve into the intricate relationships between these partial differential equations and subvarieties, examining their theoretical framework and geometric interpretations. Learn about recent developments in the field through a systematic survey that covers key concepts, methodologies, and current research directions. Gain insights into how generalized Monge-Ampère equations extend classical theory and their significance in modern differential geometry and algebraic geometry. Discover the connections between these equations and various geometric structures, including their role in understanding complex manifolds and their applications in solving geometric problems involving subvarieties.