トポロジー火曜セミナー

過去の記録 ~05/01次回の予定今後の予定 05/02~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河澄 響矢, 北山 貴裕, 逆井卓也, 葉廣和夫
セミナーURL https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html

2025年04月22日(火)

17:30-18:30   数理科学研究科棟(駒場) hybrid/056号室
Lie 群論・表現論セミナーと合同。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
奥田 隆幸 氏 (広島大学)
Coarse coding theory and discontinuous groups on homogeneous spaces (JAPANESE)
[ 講演概要 ]
Let $M$ and $\mathcal{I}$ be sets, and consider a surjective map
\[ R : M \times M \to \mathcal{I}. \]
For each subset $\mathcal{A} \subseteq \mathcal{I}$, we define $\mathcal{A}$-free codes on $M$ as subsets $C \subseteq M$ satisfying
\[ R(C \times C) \cap \mathcal{A} = \emptyset. \]
This definition encompasses various types of codes, including error-correcting codes, spherical codes, and those defined on association schemes or homogeneous spaces. In this talk, we introduce a "pre-bornological coarse structure" on $\mathcal{I}$ and define the notion of coarsely $\mathcal{A}$-free codes on $M$. This extends the concept of $\mathcal{A}$-free codes introduced above. As a main result, we establish relationships between coarse coding theory on Riemannian homogeneous spaces $M = G/K$ and discontinuous group theory on non-Riemannian homogeneous spaces $X = G/H$.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html