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Title: Analytic Combinatorics, Rigorous Numerics, and Uniqueness of Biomembranes

Speaker: Steve Melczer Affiliation: University of Waterloo Zoom: Contact Karen Yeats

Abstract:

Since the invention of the compound microscope in the early seventeenth century, scientists have marvelled over red blood cells and their surprising shape. An influential model of Canham predicts the shapes of blood cells and similar biomembranes come from a variational problem minimizing the "bending energy" of these surfaces. Because observed (healthy) cells have the same shape in humans, it is natural to ask whether the model admits a unique solution. Here, we prove solution uniqueness for the genus one Canham problem.