Optimal Shape of Tree Roots and Branches - Seminar in Analysis and Methods of PDE

Explore the fascinating world of optimal shapes in nature through this 56-minute seminar presented by Alberto Bressan from Penn State University. Delve into the mathematical perspective of how living organisms evolve to achieve their "best possible" shape. Examine two key functionals: the "sunlight functional" for modeling sunlight capture by tree leaves, and the "harvest functional" for nutrient collection by roots. Investigate how these functionals interact with the "ramified transportation cost" for nutrient movement within the tree. Learn about the semicontinuity of these functionals, the existence and properties of optimal solutions in measure spaces, and discuss open problems including computational challenges and parameter dependencies. Gain insights into this cutting-edge research that bridges mathematics with biological evolution, presented as part of the Society for Industrial and Applied Mathematics' online seminar series.