The Universal Beltrami Equation and Its Interaction with the Monge-Ampère Equation and the Scaling Limits of Random Structures

Explore the universal Beltrami equation and its fascinating connections to the Monge-Ampère equation and scaling limits of random structures in this 48-minute conference talk by Kari Astala from the University of Helsinki, presented at the Fields Institute as part of the Fields-CNAM Nonlinear Days 2025 conference on Structures and Processes: Dynamical, Geometric, and Random. Delve into advanced mathematical concepts that bridge partial differential equations with probabilistic structures, examining how these fundamental equations interact and influence the behavior of complex mathematical systems. Gain insights into cutting-edge research that connects geometric analysis with random processes, understanding the theoretical foundations and applications of these mathematical relationships. Note that technical difficulties resulted in the first few minutes not being recorded properly, but the majority of this comprehensive mathematical presentation remains intact for detailed study of these sophisticated mathematical concepts.