Explore the geometric stability of Weyl's law and its applications to asymptotic spectral shape optimization in this 49-minute seminar by Sam Farrington from the Centre de recherches mathématiques (CRM). Delve into the Weyl asymptotic formula for Dirichlet and Neumann eigenvalues of bounded Lipschitz domains, examining conditions for stability in sequences of domains. Investigate the asymptotic behavior of eigenvalue suprema and infima over collections of bounded Lipschitz domains. Learn about proofs for bounded convex domains and their applications in spectral shape optimization problems. Discover insights on minimizing Dirichlet, Neumann, and mixed Dirichlet-Neumann eigenvalues for convex domains with prescribed perimeter or diameter.