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Mathematical Sciences-Discrete Mathematics Seminar-Ada Chan (York University) "Fractional revival on graphs"

Wednesday, February 26, 2020
10:00 am

Location:

Floor/Room #: 
203

Speaker: Ada Chan, York University "Title TBA"
Title: "Fractional revival on graphs"
Abstract: Let X be a weighted graph and A be its adjacency matrix. The continuous-time quantum walk on X is given be the transition matrix e-i t A. Let ea and eb denote the characteristic vectors of a and b in V(X). We say fractional revival occurs from vertex a to b at time τ if
e-i τ A ea = α ea+β eb,
for some complex numbers α and β satisfying |α|2 +|β|2=1.

When α=0, we have perfect state transfer from a to b. The spectral properties of graphs admitting perfect state transfer have been studied extensively in the past decade. In particular, perfect state transfer occurs only between strongly cospectral vertices.

In this talk, we extend the notion of strong cospectrality to a necessary spectral condition on vertices having fractional revival. We give a characterization of graphs admitting fractional revival, and construct weighted graphs that have fractional revival between every pair of vertices.

This is joint work with Gabriel Coutinho, Whitney Drazen, Or Eisenberg, Chris Godsil, Mark Kempton, Gabor Lippner, Christino Tamon and Hanmeng Zhan.