CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici 2022

Intrinsic Diophantine approximation on circles and spheres

speaker: Dong Han Kim (Dongguk University)

abstract: We study Lagrange spectra arising from intrinsic Diophantine approximation of copies of a circle and a sphere. More precisely, we consider three copies of a unit circle embedded in $\mathbb{R}2$ or $\mathbb{R}3$ and three copies of a unit sphere embedded in $\mathbb{R}3$ or $\mathbb{R}4$. We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of $\mathbb{R}$ and $\mathbb{C}$. Combining this with prior work of Asmus L.~Schmidt on the spectra of $\mathbb{R}$ and $\mathbb{C}$, we can characterize, for each of the six spectra, the smallest accumulation point and the initial discrete part leading up to it completely. This is joint work with Byungchul Cha.

Tue 28 Jun, 9:15 - 10:15, Sala Conferenze Centro De Giorgi
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