Learn about point vortex confinement in simply connected domains through this mathematical lecture delivered by Shengyi Shen from Ningbo University at the Fields Institute. Explore the theoretical foundations and mathematical analysis of how point vortices behave when confined within bounded regions, examining the dynamics and constraints that arise in simply connected domains. Delve into the nonlinear dynamics and partial differential equations that govern vortex motion, understanding the mathematical framework used to describe these complex fluid mechanical phenomena. Gain insights into the intersection of fluid dynamics, mathematical analysis, and geometric constraints as they apply to vortex confinement problems. This presentation forms part of the broader thematic program on shocks and singularities in nonlinear evolution equations, connecting vortex dynamics to wider applications in physical and life sciences.