Shankar Venkataramani - On branch points and C^{1,1} pseudospherical immersions

This is a report of joint work with Toby Shearman. The key result is that one can define a (local) winding number of the Gauss Map for C^{1,1} hyperbolic surfaces in R^3 and this degree is an obstruction for approximation by smooth immersions in $W^{2,2}_{loc}$. I will discuss the ideas behind the proof, as well as the motivation for studying this question, which comes from the mechanics of non-Euclidean plates.