Speaker:
John Gemmer,  Brown University

Title: 
Isometric Immersions and Pattern Formation in Thin Elastic Sheets

Abstract: 
Swelling thin elastic sheets are archetypical examples of pattern forming systems which are often modeled as the minimum an elastic energy which is the sum of a strong stretching energy which penalizes deviations from a growth induced geometry and a weak bending energy. A fundamental question is whether we can deduce the three dimensional configuration of the sheet given exact knowledge of the swelling pattern. Using a combination of analysis and numerical conjectures I will argue that the periodic patterns observed in nature correspond to low energy isometric immersions of an imposed geometry.