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トポロジー火曜セミナー
過去の記録 ～03/17｜次回の予定｜今後の予定 03/18～
| 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 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2024年06月20日(木)
17:00-18:30 数理科学研究科棟(駒場) 002号室
RIKEN iTHEMS との共同開催。開催日、開催場所にご注意下さい。対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Dominik Inauen 氏 (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
RIKEN iTHEMS との共同開催。開催日、開催場所にご注意下さい。対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Dominik Inauen 氏 (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
[ 講演概要 ]
The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
[ 参考URL ]The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
