Title: Theoretical Models of Shape Formation: Analysis, Geometry and Energy Scaling Laws
Speaker: Marta Lewicka
Speaker Info: University of Pittsburgh
Special Note: Note that the talk starts 4pm, not at 4.10pm!
Recently, there has been sustained interest in the growth-induced morphogenesis, particularly of low-dimensional structures such as filaments, laminae and their assemblies, which arise routinely in biological systems and their artificial mimics. While the related questions lie at the interface of biology, chemistry and physics, fundamentally they have a deeply geometric and analytical character and may be seen as a variation on a classical theme in differential geometry - that of embedding a shape with a given metric. A possible analysis uses the variational point of view, namely the model of 3d non-Euclidean elastic energy which measures the deviation of the given deformation from orientation preserving realizations of the prescribed metric.Date: Wednesday, December 04, 2013
I will give an overview of available results in this setting, including the study of Sobolev spaces of infinitesimal isometries, their density and matching properties, the scaling analysis of energy minimizers, and the derivation of the a hierarchy of variational limits, which are differentiated by the embeddability properties of the prescribed metric.