Séminaire Géométrie et groupes discrets
# Rational Approximations to Linear Subspaces

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Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

Dirichlet's theorem in Diophantine approximation implies that for any real x, there exists a rational p/q arbitrarily close to x such that |x-p/q| < 1/q^{2}. In addition, the exponent 2 that appears in this inequality is optimal, as seen for example by taking $x=\sqrt2$. In 1967, Wolfgang Schmidt suggested a similar problem, where x is a real subspace of R^{d} of dimension ℓ, which one seeks to approximate by a rational subspace v. Our goal will be to obtain the optimal value of the exponent in the analogue of Dirichlet's theorem within this framework. The proof is based on a study of diagonal orbits in the space of lattices in R^{d}.

Organized by

Fanny Kassel

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