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SUMMARY:Matthew Jenssen (University of Birmingham)
DTSTART:20200608T130000Z
DTEND:20200608T140000Z
DTSTAMP:20260404T145133Z
UID:EPC/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/EPC/9
 /">A proof of the Upper Matching Conjecture for large graphs</a>\nby Matth
 ew Jenssen (University of Birmingham) as part of Extremal and probabilisti
 c combinatorics webinar\n\n\nAbstract\nWe show that the `Upper Matching Co
 njecture' of Friedland\, Krop\, and Markström and the analogous conjectur
 e of Kahn for independent sets in regular graphs hold for all large enough
  graphs as a function of the degree. That is\, for every $d$ and every lar
 ge enough $n$ divisible by $2d$\, a union of $n \\over 2d$ copies of the c
 omplete $d$-regular bipartite graph maximises the number of independent se
 ts and matchings of any given size over all $d$-regular graphs on $n$ vert
 ices. For the proof\, we'll discuss two different approaches to these prob
 lems\, both inspired by statistical physics. This is joint work with Ewan 
 Davies and Will Perkins.\n
LOCATION:https://stable.researchseminars.org/talk/EPC/9/
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