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解析学火曜セミナー
過去の記録 ～05/18｜次回の予定｜今後の予定 05/19～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 156号室 |
|---|---|
| 担当者 | 石毛 和弘, 坂井 秀隆, 伊藤 健一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
2016年12月06日(火)
16:50-18:20 数理科学研究科棟(駒場) 126号室
Horia Cornean 氏 (オールボー大学、デンマーク)
On the trivialization of Bloch bundles and the construction of localized Wannier functions (English)
Horia Cornean 氏 (オールボー大学、デンマーク)
On the trivialization of Bloch bundles and the construction of localized Wannier functions (English)
[ 講演概要 ]
We shall present an introductory lecture on the trivialization of Bloch bundles and its physical implications. Simply stated, the main question we want to answer is the following: given a rank $N＼geq 1$ family of orthogonal projections $P(k)$ where $k＼in ＼mathbb{R}^d$, $P(＼cdot)$ is smooth and $＼mathbb{Z}^d$-periodic, is it possible to construct an orthonormal basis of its range which consists of vectors which are both smooth and periodic in $k$? We shall explain in detail the connection with solid state physics. This is joint work with I. Herbst and G. Nenciu.
We shall present an introductory lecture on the trivialization of Bloch bundles and its physical implications. Simply stated, the main question we want to answer is the following: given a rank $N＼geq 1$ family of orthogonal projections $P(k)$ where $k＼in ＼mathbb{R}^d$, $P(＼cdot)$ is smooth and $＼mathbb{Z}^d$-periodic, is it possible to construct an orthonormal basis of its range which consists of vectors which are both smooth and periodic in $k$? We shall explain in detail the connection with solid state physics. This is joint work with I. Herbst and G. Nenciu.
