Coarse coding theory and discontinuous groups for homogeneous spaces
開催期間
16:00 ~ 17:30
場所
講演者
概要
【講演要旨】Let $M$ and $\mathcal{I}$ be both sets, and fix a surjective map $R: M \times M \to \mathcal{I}$. Then, for each subset $\mathcal{A}$ of $\mathcal{I}$, $\mathcal{A}$-free-codes on $M$ are defined as subsets $C$ of $M$ with $R(C \times C) \cap \mathcal{A} = \emptyset$. This definition of codes
encompasses error-correcting codes, spherical codes, and other codes defined on association schemes or
homogeneous spaces.
In this talk, we fix a "pre-bornological coarse structure" on the set $\mathcal{I}$, and give a definition of "coarsely $\mathcal{A}$-free-
codes" on $M$. This provides a generalization of the concept of $\mathcal{A}$-free-codes as mentioned above. As the main
result, we will discuss the relationships between coarse coding theory on Riemannian homogeneous spaces
$M = G/K$ and discontinuous group theory on non-Riemannian homogeneous spaces $X = G/H$.