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Department of Mathematical SciencesDiscrete Math SeminarTuesday, October 28th, 20254:00PM-4:50PMOlin Hall 126Speaker: Bill Martin, WPITitle: Triple intersection numbers and Q-ideals of Paley graphs Abstract: In joint work with Andries Brouwer, we used the Hasse-Weil bound for elliptic curves to estimate triple intersection numbers for the Paley graphs. This allows us to build a nice generating set for the ideal of all polynomials that vanish on each column of an eigenprojector of the adjacency matrix of the graph. This involves joint work with Ethan Washock (WPI Mac ’22). As time permits, I will provide some context for this question and a conjecture about the ``dual girth’’ of a Q-polynomial (co-metric) association scheme.

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