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SUMMARY:Justin Salez (Université Paris-Dauphine)
DTSTART:20210611T120000Z
DTEND:20210611T130000Z
DTSTAMP:20260423T024536Z
UID:MEGA/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MEGA/20/">Sp
 arse expanders have negative curvature</a>\nby Justin Salez (Université P
 aris-Dauphine) as part of Séminaire MEGA\n\n\nAbstract\nWe prove that bou
 nded-degree expanders with non-negative Ollivier-Ricci curvature do not ex
 ist\, thereby solving a long-standing open problem suggested by Naor and M
 ilman and publicized by Ollivier (2010). In fact\, this remains true even 
 if we allow for a vanishing proportion of large degrees\, large eigenvalue
 s\, and negatively-curved edges. To establish this\, we work directly at t
 he level of Benjamini-Schramm limits\, and exploit the entropic characteri
 zation of the Liouville property on stationary random graphs to show that 
 non-negative curvature and spectral expansion are incompatible “at infin
 ity”. We then transfer this result to finite graphs via local weak conve
 rgence. The same approach applies to the Bakry-Émery curvature condition 
 CD(0\, ∞)\, thereby settling a recent conjecture of Cushing\, Liu and Pe
 yerimhoff (2019).\n
LOCATION:https://researchseminars.org/talk/MEGA/20/
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