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Singular vectors play a crucial role in the study of Diophantine approximation. I want to discuss about the inheritance of the measure zero property of the set of singular vectors in R^n. I will also talk about a sufficient and necessary condition on hyperplanes such that almost all vectors in the hyperplanes are not singular.
On a slightly different direction I want to briefly talk about about some simple yet surprising results on ψ-Dirichlet numbers and singular vectors in function field. The talk will be based on joint works with Yewei Xu.