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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-thomas-jung-spier
SUMMARY:Tutte colloquium-Thomás Jung Spier
CLASS:PUBLIC
DESCRIPTION:Summary \n\nSum of squares of positive eigenvalues\n\nSpeaker\n
  Thomás Jung Spier\n\nAffiliation\n University of À¶Ý®ÊÓƵ\n\nLocation\n 
 MC 5501\n\nThe spectral Turán theorem says that if a graph has largest\ne
 igenvalue $\\lambda_1$\, $m$ edges and clique number $\\omega$\, then\n$\\
 lambda_1^2 \\leq 2m (1-\\frac{1}{\\omega})$. This result implies the\nclas
 sical Turán bound $m \\leq (1-\\frac{1}{\\omega})\\frac{n^2}{2}$.\nIn thi
 s talk\, we present the proof of the Wocjan\, Elphick and\nAnekstein conje
 cture in which\, in the spectral Turán bound\, the\nsquare of the first e
 igenvalue is replaced by the sum of the squares\nof the positive eigenvalu
 es and the clique number is replaced by the\nvector chromatic number. \nW
 e will also present recent progress towards a conjecture by Bollobás\nand
  Nikiforov in which\, in the spectral Turán bound\, the square of\nthe fi
 rst eigenvalue is replaced by the sum of the squares of the two\nlargest e
 igenvalues. This is joint work with Gabriel Coutinho and\nShengtong Zhang.
 \n 
DTSTAMP:20250516T165921Z
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