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CATEGORIES:Analysis Seminar
SUMMARY:Mapping n grid points onto a square forces an arbi
trarily large Lipschitz constant. - Michael Dymond
(Innsbruck)
DTSTART:20190227T100000Z
DTEND:20190227T110000Z
UID:TALK3637AT
URL:/talk/index/3637
DESCRIPTION:We discuss a recent work which proves that the reg
ular nxn square grid of points in the integer lat
tice ZxZ cannot be recovered from an arbitrary n2-
element subset of ZxZ via a mapping with prescribe
d Lipschitz constant (independent of n). This answ
ers negatively a question of Feige. Our resolution
of Feige's question takes place largely in a cont
inuous\nsetting and is based on some new results f
or Lipschitz mappings falling into two broad areas
of interest\, which we study independently. First
ly we discuss Lipschitz regular mappings on Euclid
ean spaces\, with emphasis on their bilipschitz de
composability in a sense comparable to that of the
well known result of Jones. Secondly\, we build o
n work of Burago and Kleiner and McMullen on non-r
ealisable densities. We verify the existence\, and
further prevalence\, of strongly non-realisable d
ensities inside spaces of continuous functions. Th
is is joint work with Vojtech Kaluza and Eva Kop
eckรก.\n
LOCATION:PHYW-SR1 (103)
CONTACT:Diogo Oliveira E Silva
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