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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240913T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-thomas-jung-spier
SUMMARY:Tutte colloquium-Thomás Jung Spier
CLASS:PUBLIC
DESCRIPTION:Sum of squares of positive eigenvalues\n\nSpeaker\n Thomás Jun
 g Spier\n\nAffiliation\n University of Waterloo\n\nLocation\n MC 5501\n\nT
 he spectral Turán theorem says that if a graph has largest\neigenvalue $\
 \lambda_1$\, $m$ edges and clique number $\\omega$\, then\n$\\lambda_1^2 \
 \leq 2m (1-\\frac{1}{\\omega})$. This result implies the\nclassical Turán
  bound $m \\leq (1-\\frac{1}{\\omega})\\frac{n^2}{2}$.\nIn this talk\, we 
 present the proof of the Wocjan\, Elphick and\nAnekstein conjecture in whi
 ch\, in the spectral Turán bound\, the\nsquare of the first eigenvalue is
  replaced by the sum of the squares\nof the positive eigenvalues and the c
 lique number is replaced by the\nvector chromatic number. \nWe will also 
 present recent progress towards a conjecture by Bollobás\nand Nikiforov i
 n which\, in the spectral Turán bound\, the square of\nthe first eigenval
 ue is replaced by the sum of the squares of the two\nlargest eigenvalues. 
 This is joint work with Gabriel Coutinho and\nShengtong Zhang.
DTSTAMP:20260405T062437Z
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