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Explore the mathematical analysis of shape optimization problems in population dynamics through this 50-minute lecture examining the principal eigenvalue of indefinite weighted problems in bounded domains. Delve into the minimization of eigenvalues to enhance population persistence, which translates into optimizing the subregion of habitats favorable to species survival. Investigate the singular limit analysis of this problem under both Dirichlet and Neumann boundary conditions when dealing with arbitrarily small favorable regions. Discover how favorable regions remain connected and concentrate at specific points determined by boundary conditions, while examining the complex relationship between the location and shape of these regions. Learn about cutting-edge research findings from collaborative work with Lorenzo Ferreri, Dario Mazzoleni, and Benedetta Pellacci, presented as part of the Thematic Programme on "Free Boundary Problems" at the Erwin Schrödinger International Institute for Mathematics and Physics.
