Speaker
Dr
Minerva Catral
(Xavier University)
Description
For vertex-labelled graphs $G$ and $H$ on $n\geq 1$ vertices, we consider matrices of the form $C(A,B) = \left[\begin{array}{c|c} A&B\\ \hline I&O\\\end{array}\right]\in\mathbb{R}^{2n\times 2n}$ where $A,B\in\mathbb{R}^{n\times n}$ are a pair of real symmetric matrices with nonzero patterns determined by the edges of the graph pair $G, H$. We denote the set of all such matrices by $\mathcal{S}(G,H)$. Our aim is to determine all possible spectra for $C(A,B)\in\mathcal{S}(G,H)$. We conjecture that $C(A,B)$ can attain any spectrum invariant under conjugation regardless of the chosen vertex-labelled graphs $G$ and $H$. In this talk, we highlight some results that support our conjecture.
Authors
Dr
Adam Berliner
(St Olaf College)
Dr
Michael Cavers
(University of Toronto)
Dr
Minerva Catral
(Xavier University)
Dr
Pauline van den Driessche
(University of Victoria)
Dr
Sooyeong Kim
(University of Guelph)