BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Andrea Braides (University of Rome Tor Vergata)
DTSTART:20200615T120000Z
DTEND:20200615T124500Z
DTSTAMP:20260423T035926Z
UID:OWMADS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWMADS/10/">
 Continuum limits of interfacial energies on (sparse and) dense graphs</a>\
 nby Andrea Braides (University of Rome Tor Vergata) as part of One World s
 eminar: Mathematical Methods for Arbitrary Data Sources (MADS)\n\n\nAbstra
 ct\nI review some results on the convergence of energies defined on graphs
 . My interest in such energies comes from models in Solid Mechanics (where
  the bonds in the graph represent the relevant atomistic interactions) or 
 Statistical Physics (Ising systems)\, but the nodes of the graph can also 
 be thought as a collection of data on which the bonds describe some relati
 on between the data.\nThe typical objective is an approximate (simplified)
  continuum description of problems of minimal cut as the number N of the n
 odes of the graphs diverges.\nIf the graphs are sparse (i.e. the number of
  bonds is much less than the total number of pairs of nodes as N goes to i
 nfinity)\, often (more precisely when we have some control on the range or
  on the decay of the interactions) such minimal-cut problems translate int
 o minimal-perimeter problems for sets or partitions on the continuum. This
  description is easily understood for periodic lattice systems\, but carri
 es on also for random distributions of nodes. In the case of a (locally) u
 niform Poisson distribution\, actually the limit minimal-cut problems are 
 described by more regular energies than in the periodic-lattice case. \nWh
 en we relax the hypothesis on the range of interactions\, the description 
 of the limit of sparse graphs becomes more complex\, as it depends subtly 
 on geometric characteristics of the graph\, and is partially understood. S
 ome easy examples show that\, even though for the continuum limit we still
  remain in a similar analytical environment\, the description as (sharp) i
 nterfacial energies can be lost in this case\, and more “diffuse” inte
 rfaces must be taken into account.\nIf instead we consider dense sequences
  of graphs (i.e.\, the number of bonds is of the same order as the total n
 umber of pairs as N goes to infinity) then a completely different limit en
 vironment must be used\, that of graphons (which are abstract limits of gr
 aphs)\, for which sophisticated combinatoric results can be used. We can r
 e-read the existing notion of convergence of graphs to graphons as a conve
 rgence of the related cut functionals to non-local energies on a simple re
 ference parameter set. This convergence provides an approximate descriptio
 n of the corresponding minimal-cup problems.\nWorks in collaboration with 
 Alicandro\, Cicalese\, Piatnitski and Solci (sparse graphs) and Cermelli a
 nd Dovetta (dense graphs).\n
LOCATION:https://researchseminars.org/talk/OWMADS/10/
END:VEVENT
END:VCALENDAR