Explore recent advancements in the linear and nonlinear stability of shear flows and vortices within two-dimensional Euler equations in this 48-minute conference talk. Delve into the main findings, including nonlinear asymptotic stability of monotonic shear flows in finite channels and point vortices in the plane, as well as linear stability of smooth decreasing vortices in the plane. Gain insights from the collaborative research of Alexandru D. Ionescu and Hao Jia, presented at the International Mathematical Union. Access accompanying presentation slides for a comprehensive understanding of this complex mathematical topic.