Title: A quantitative approach to quadratic embedding of graphs
Speaker: Nobuaki Obata (Tohoku University, Japan)
Speaker's URL: https://www.math.is.tohoku.ac.jp/~obata/english/
Abstract: It is known in the Euclidean distance geometry tracing back to Schoenberg (1935-37) that a graph admits a quadratic embedding in a Euclidean space if and only if the distance matrix
$D=[d(x,y)]$ is conditionally negative definite. This condition, being equivalent to that the q-matrix $Q=[q^{d(x,y)}]$ is positive definite for all $0\le q\le 1$, appears also in quantum probability. A new numerical invariant of a graph called the quadratic embedding constant (QEC) was introduced in 2017 for a quantitative approach.
In this talk we will review the basic ideas and recent results and propose some questions.
References: arXiv:2207.13278, arXiv:2206.05848, arXiv:1904.08059
URL associated with Seminar: https://u.osu.edu/aots/
