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DTSTART;TZID=America/Toronto:20240205T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-chris-godsil-11
SUMMARY:Algebraic Graph Theory - Chris Godsil
CLASS:PUBLIC
DESCRIPTION:TITLE: Laplacian State Transfer\n\nSPEAKER:\n Chris Godsil\n\nA
 FFILIATION:\n University of Waterloo\n\nLOCATION:\n Please contact Sabrin
 a Lato for Zoom link.\n\nABSTRACT: Let $X$ be a graph and let $E_1\,\\ldo
 ts\,E_d$ be the spectral\nidempotents of its adjacency matrix. If $a$ and 
 $b$ are vertices in\n$X$\, they are \\textsl{strongly cospectral} if $E_re
 _ae_a^TE_r =\nE_re_be_b^T$ for each $r$. This is a relation between the tw
 o density\nmatrices $e_aa_a^T$ and $e_be_b^T$\, and is a necessary conditi
 on for\nstate transfer between pure states.\n\nIf $L$ is the Laplacian of 
 a graph $X$ with $m$ edges\, the matrix\n$(1/2m)L$ is positive semidefinit
 e with trace one\, thus it is a\ndensity matrix. We call it a \\textsl{Lap
 lacian state}. It is pure only\nif $X$ is an edge. We have been investigat
 ing transfer between\nLaplacian states in continuous quantum walks. We hav
 e extended the\ndefinition of strongly cospectral to this case\, have obta
 ined a number\nof results are about various forms of state transfer. My ta
 lk will be\na report on this.\n\n(This is joint work with Ada Chan\, Qiuti
 ng Chen\, Wanting Sun and\nXiaohong Zhang.)
DTSTAMP:20260404T153328Z
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