DSNT Seminarium: Rational approximation on spheres

Abstract:
Classical diophantine approximation intends to quantify the density of rational numbers in Euclidean spaces. In recent years there have been some interest in intrinsic diophantine approximation, where one considers an algebraic variety with a dense set of rational points and aims to prove analogues of the classical results, such as Dirichlet’s theorem, Khinchin-Groshev theorem, Dani correspondence etc. A general theory in this case still eludes mathematicians. In this talk we will focus on spheres, compare and contrast it with the classical case and mention some recent developments.

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