Robin Green Functions and the Shape of Lungs

This lecture explores the mathematical modeling of mammalian lung shapes through the study of diffusions with partially reflective (Robin) boundary conditions in rough domains. Discover how Robin solutions differ significantly from completely absorbing (Dirichlet) boundary conditions, as they behave like Dirichlet solutions averaged at a scale dependent on reflection probability. Learn about the rigorous mathematical proofs behind observed properties of lungs, including their self-similarity dimension and oxygen absorption changes relative to reflection parameters. The presentation covers ongoing joint research with G. David, S. Decio, M. Filoche, S. Mayboroda, and M. Michetti, connecting advanced mathematical concepts to biological structures.