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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium


Shankar Venkataramani
University of Arizona
Title: Non-euclidean elasticity, discrete differential geometry and a quantitative Hilbert's theorem

Abstract: Leaves, flowers and torn plastic bags are all examples of thin objects that are conjectured to have no stress-free configurations in $R^3$. Non-euclidean elasticity is the study of energy driven pattern formation in such objects. I will discuss some recent analytic, geometric and numerical approaches to this problem, and discuss some of the intriguing results including (i) the occurrence of "geometric" defects that are invisible to the energy, but play a crucial role in determining the global morphology, (ii) a generalization of the Sine-Gordon equation to describe "rough" hyperbolic surfaces with constant negative curvature, and (iii) the important role of regularity in quantitative versions of the Hilbert-Efimov theorem on the nonexistence of $C^2$ isometric immersions of the Hyperbolic plane into $R^3$.

This is joint work with Toby Shearman (U. Arizona) and John Gemmer (Wake Forest).

Date: Tuesday, October 24, 2017
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice