Delio Mugnolo: Non-canonical connectivity measures on metric graphs

(26 fèvrier 2024/February 26, 2024) Seminar Spectral Geometry in the clouds.
https://archimede.mat.ulaval.ca/agiro...

Delio Mugnolo: Non-canonical connectivity measures on metric graphs
Abstract: Fiedler proposed the “algebraic connectivity” – i.e., the spectral gap of the graph Laplacian – as a measure of connectivity of discrete graphs; an analogous idea was substantiated by a two-sided bound on the spectral gap of the metric graph Laplacian obtained by Nicaise (1987) and KennedyKurasov-Malenov´a-Mugnolo (2016). Further, possibly “more geometric” quantities can be shown to describe the connectivity of a metric graph, too. I will focus on the mean distance, a rather natural quantity that can be defined on each compact metric measure space. After presenting geometric bounds on this quantity, I will show its interplay with the spectral gap of the metric graph Laplacian and outline some similarities with the Kohler-Jobin inequality for metric graphs. This is joint work with Luis Baptista and James B. Kennedy.