Explore the intricacies of fluid dynamics in this 57-minute seminar on Analysis and Geometry, presented by Dallas Albritton from the School of Mathematics at the Institute for Advanced Study. Delve into the complex world of Navier-Stokes equations, focusing on the non-uniqueness of Leray solutions in forced scenarios. Follow the progression from introduction to the main theorem, examining concepts such as suitable weak solutions, unstable manifolds, and similarity variables. Investigate two-dimensional instability, the construction of unstable vortices, and neutral limiting modes. Venture into three-dimensional territory with discussions on vortex rings and axis-symmetric Euler equations. Gain insights into linearized Euler operators and single function spaces, concluding with a thought-provoking question-and-answer session.