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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.

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