A theme of Diophantine approximation is to see if a Diophantine property gets inherited by a sub-manifold from its ambient affine subspace. We will talk about one such property, called as singularity of vectors, in case of sub-manifolds of Rn and function field over finite fields. One reason why singular vectors are an interesting object of study is their connection with homogeneous dynamics, in particular they correspond to some divergent orbits. The talk will be based on a joint work with Yewei Xu, who was my REU student in last summer. Speaker(s): Shreyasi Datta (U Michigan)