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DTSTART;TZID=America/Toronto:20220916T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-lap-chi-lau-0
SUMMARY:Tutte Colloquium - Lap Chi Lau
CLASS:PUBLIC
DESCRIPTION:TITLE: Cheeger Inequalities for Vertex Expansion and Reweighted
 \nEigenvalues\n\nSpeaker:\n Lap Chi Lau\n\nAffiliation:\n University of Wa
 terloo\n\nLocation:\n MC 5501\n\nABSTRACT: \n\nThe classical Cheeger's ine
 quality relates the edge conductance $\\phi$\nof a graph and the second sm
 allest eigenvalue $\\lambda_2$ of the\nLaplacian matrix. Recently\, Oleske
 r-Taylor and Zanetti discovered a\nCheeger-type inequality $\\psi^2 / \\lo
 g |V| \\lesssim \\lambda_2^*\n\\lesssim \\psi$ connecting the vertex expan
 sion $\\psi$ of a graph\n$G=(V\,E)$ and the maximum reweighted second smal
 lest eigenvalue\n$\\lambda_2^*$ of the Laplacian matrix. In this work\, we
  first improve\ntheir result to $\\psi^2 / \\log d \\lesssim \\lambda_2^* 
 \\lesssim \\psi$\nwhere $d$ is the maximum degree in $G$\, which is optima
 l assuming the\nsmall-set expansion conjecture. Also\, the improved result
  holds for\nweighted vertex expansion\, answering an open question by\nOle
 sker-Taylor and Zanetti. 
DTSTAMP:20260406T204438Z
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