月曜解析セミナー: Does diffusion determine the geometry?

開催日時
2017年   7月 24日 15時 00分 ~ 2017年   7月 24日 16時 30分
場所
理学部3号館210
講演者
Marcel Schmidt (Mathematical Institute Friedrich-Schiller-Universität)
 
Can one hear the shape of a drum? In mathematical terms this famous question of M. Kac asks whether two unitarily equivalent Laplacians live on the same geometric object. It is now known, that the answer to this question is negative in general.

Following an idea of Wolfgang Arendt, we replace the unitary transformation intertwining the Laplacians by an order preserving one and then ask how much of the geometry is preserved. In this situation the associated semigroups, which encode diffusion, are equivalent up to an order isomorphism. Therefore, the question becomes as stated in the title and we try to provide an answer in great generality. In particular, we discuss the situation for graph Laplacians and Laplacians on metric measure spaces. (this is joint work with Matthias Keller, Daniel Lenz and Melchior Wirth)

定例時間変更.14:45--18:00の中で講演ごとに設定.


関連項目

研究集会・セミナー・集中講義の一覧へ