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SUMMARY:Lina Li (University of Illinois at Urbana-Champaign)
DTSTART:20200625T020000Z
DTEND:20200625T030000Z
DTSTAMP:20260423T035023Z
UID:SCMSComb/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SCMSComb/4/"
 >Independent sets in middle two layers of Boolean lattice</a>\nby Lina Li 
 (University of Illinois at Urbana-Champaign) as part of SCMS Combinatorics
  Seminar\n\n\nAbstract\nIn recent decades\, independent sets in the discre
 te hypercube has received a lot of attention from many notable researchers
 .\nThe classical result of Korshunov and Sapozhenko in 1983 counts the num
 ber of independent sets in the hypercube\, and then shows that typical ind
 ependent sets are not far from the trivial construction.\nFor an odd integ
 er $n=2d-1$\, let $\\mathcal{B}(n\, d)$ be the subgraph of the hypercube i
 nduced by the two largest layers. \nOur new results describe the typical s
 tructure of independent sets in $\\mathcal{B}(n\, d)$ and also give precis
 e asymptotics on the number of them.\nThe proofs use Sapozhenko's graph co
 ntainer lemma\, and a recently developed method of Jenssen and Perkins\, w
 hich combines Sapozhenko's graph container lemma with a classcal tool from
  statistical physics\, the cluster expansion for polymer models.\nThis is 
 a joint work with with Jozsef Balogh and Ramon I. Garcia.\n\nPassword 0168
 01\n
LOCATION:https://researchseminars.org/talk/SCMSComb/4/
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