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Tuesday, June 28, 2016

**Abstract:** A Sobolev space consists of integrable functions $f:X\to Y$ with integrable derivative, where $X$ and $Y$ are "sufficiently'' Euclidean manifolds. One can naturally define metrics on these spaces, leading one to ask the following question: Are "nice'' functions dense in a Sobolev space? Here, "nice'' depends on $X$ and $Y$ and may refer to smooth, Lipschitz, etc. In this talk, I will introduce Sobolev spaces between manifolds and discuss my current research of investigating the density of Lipschitz functions in Sobolev spaces of functions from balls to a class of sub-Riemannian manifolds, Jet spaces.