Approximation of linear subspaces by rational linear subspaces

Abstract: We elaborate on a problem raised by Schmidt in 1967: rational approximation of linear subspaces of $\mathbb{R}^n$. In order to study the quality approximation of irrational numbers by rational ones, one can introduce the exponent of irrationality of a number. We can then generalize this notion in the framework of vector subspaces for the approximation of a subspace by so-called rational subspaces.

After briefly introducing the tools for constructing this generalization, I will present the different possible studies of this object. Finally I will explain how we can construct spaces with prescribed exponents.

dynamical systemsnumber theory

Audience: researchers in the topic

One World Numeration seminar

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