東大数値解析セミナー (UTNAS) 第158回

東京大学大学院数理科学研究科と情報理工学系研究科では,本年度も数値解析セミナーを定期的(月に1,2回程度)に開催致します.
多くの皆様のご参加をお待ち申し上げます.

講演者
Dorin Bucur (Université Savoie Mont Blanc)

題目
On polygonal nonlocal isoperimetric inequalities: Hardy-Littlewood, Riesz, Faber-Krahn

概要
The starting point is the Faber-Krahn inequality on the first eigenvalue of the Dirichlet Laplacian.
Many refinements were obtained in the last years, mainly due to the use of recent techniques based on the analysis of vectorial free boundary problems.
It turns out that the polygonal version of this inequality, very easy to state, is extremely hard to prove and remains open since 1947, when it was conjectured by Polya.
I will connect this question to somehow easier problems, like polygonal versions of Hardy-Littlewood and Riesz inequalities and I will discuss the local minimality of regular polygons and the possibility to prove the conjecture by a mixed approach.
This talk is based on joint works with Beniamin Bogosel and Ilaria Fragala.