DisCoMath Seminar: The Strong Spectral Property and the Strong Multiplicity Property
Discrete & Computational Math Seminar (DisCoMath)
The Strong Spectral Property and the Strong Multiplicity Property
Dr. Brendan Rooney
Assistant Professor
School of Mathematical Sciences, RIT
Abstract:
This talk is the second in a series of two talks on "strong" matrix conditions. In this talk we focus on two analogous properties to the Strong Arnold Property, and their connection to the minimum number of distinct eigenvalues of a graph. For a graph G on n vertices, S(G) is the space of n×n symmetric matrices whose off-diagonal zero pattern exactly matches that of A(G). We are interested in finding q(G), the minimum number of distinct eigenvalues of a matrix M∈ S (G). A matrix M has the Strong Spectral Property (SSP) if a pair of manifolds associated with M intersect transversally at M. We will unpick what this means, and see how it can be used to give a lower bound of q(G). Our discussion follows two papers of Barrett et al., "Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph" (2016), and "The inverse eigenvalue problem of a graph: Multiplicities and minors" (2017).
Speaker Bio:
Dr. Rooney is an Assistant Professor in the School of Mathematical Sciences at RIT. He completed his Ph.D. in Combinatorics and Optimization at the University of Waterloo, Ontario, Canada. Prior to joining RIT, he was a Visiting Assistant Professor in the Department of Mathematical Sciences at Korea Advanced Institute of Science and Technology (KAIST) for three years. Dr. Rooney’s research interests include Graph Theory, Combinatorics and Combinatorial Optimization.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
Keep up with DisCoMath Seminars on the DisCoMathS webpage.
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Event Snapshot
When and Where
Who
Open to the Public
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No