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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20240927T153000
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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-eric-blais
SUMMARY:Tutte colloquium-Eric Blais
CLASS:PUBLIC
DESCRIPTION:Summary \n\nGraph Property Testing using the Container Method\n
 \nSPEAKER:\n Eric Blais\n\nAFFILATION:\n University of À¶Ý®ÊÓƵ\n\nLOCATIO
 N:\n MC 5501\n\nABSTRACT: The Graph and Hypergraph Container Methods have 
 recently\nbeen used to obtain multiple striking results across different a
 reas\nof mathematics. In this talk\, we will see how the graph container\n
 method is particularly well-suited for the study of some fundamental\nprob
 lems in graph property testing.\n\nThe main problem we will discuss in the
  talk is the Independent Set\nTesting problem introduced by Goldreich\, Go
 ldwasser\, and Ron (1998).\nIn this problem\, we are given oracle access t
 o a graph on $n$ vertices\nthat either (i) contains an independent set on 
 $\\rho n$ vertices\, or\n(ii) is $\\epsilon$-far from the property in the 
 sense that at least\n$\\epsilon n^2$ edges must be removed from the graph 
 to make it have an\nindependent set of this size. We will introduce a new 
 container lemma\nfor the latter class of graphs and we will show how this 
 lemma can be\nused to obtain a near-optimal solution to the Independent Se
 t Testing\nproblem. We will also discuss how variants and extensions of th
 e new\ncontainer lemma can be used to prove a variety of other results in\
 nproperty testing.\n\nThis is joint work with Cameron Seth.\n 
DTSTAMP:20250711T084946Z
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