When
Student: Ari Bormanis, Program in Applied Mathematics
Title: The Curly Geometry of Nature: Discrete Models and Energetic Bounds of Branched Elastic Surfaces
Advisors: Shankar Venkataramani, Math Department
Location: Math 501 | Zoom link: https://arizona.zoom.us/j/89467805641
Abstract: The natural world is filled with a rich variety of beautiful, complex, and curly forms, from flower petals to the feet of sea slugs. Why do such forms arise, and how can we model them? We take a variational perspective, modeling the surfaces we observe in nature as the minimizers of an elastic energy functional, and approach this problem from both a discrete and continuous viewpoint. The discrete theory is a fascinating object of study in its own right and fundamentally informs the proofs of our continuous methods. To this end, we propose a novel discrete algorithm that yields new tools for modeling natural forms and provides deeper insight into the continuous problem. Finally, we rigorously prove an energetic bound conjectured in previous work. This bound demonstrates that the curly surfaces of nature are better approximate minimizers of our elastic energy functional than surfaces with “smoother” boundaries, validating our approach.