BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Sabre//Sabre VObject 4.5.8//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:Europe/Zurich
X-LIC-LOCATION:Europe/Zurich
TZURL:http://tzurl.org/zoneinfo/Europe/Zurich
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19810329T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19961027T030000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:news516@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190104T234043
DTSTART;TZID=Europe/Zurich:20120328T151500
SUMMARY:Seminar Analysis: Sara Daneri (University of Zurich)
DESCRIPTION:We consider the optimal transportation problem with cost functi
 ons given by generic convex norms in Rd and absolutely continuous first ma
 rginals. We show the existence of a partition of Rd into k-dimensional set
 s\, k=0\,...\,d\, such that every optimal transport plan can be characteri
 zed\, via disintegration of measures\, as a family of optimal transport pl
 ans each moving a conditional probability of the first marginal inside one
  of these k-dimensional sets\, along the directions of an extremal k-dimen
 sional cone of the convex norm.  Moreover\, the conditional probabilities
  of the first marginal on these sets are absolutely continuous with respec
 t to the k-dimensional Hausdorff measure on the k-dimensional sets on whic
 h they are concentrated\, thus settling the longstanding Sudakov's problem
  of the existence of locally affine decompositions of Rd that reduce norm 
 cost transportation problem to families of lower dimensional ones. Finally
 \, due to the minimality of our partition with respect to this "dimensiona
 l reduction" property\, applications to secondary cost functions obtained 
 first minimizing with respect to a convex norm and then with respect to a 
 finer one (e.g.\, a strictly convex one) will be shown. These results were
  obtained in collaboration with  Stefano Bianchini (SISSA\, Trieste).
X-ALT-DESC: \nWe consider the optimal transportation problem with cost func
 tions given by generic convex norms in <b>R</b><sup>d</sup> and absolutely
  continuous first marginals. We show the existence of a partition of <b>R<
 /b><sup>d</sup> into k-dimensional sets\, k=0\,...\,d\, such that every op
 timal transport plan can be characterized\, via disintegration of measures
 \, as a family of optimal transport plans each moving a conditional probab
 ility of the first marginal inside one of these k-dimensional sets\, along
  the directions of an extremal k-dimensional cone of the convex norm.&nbsp
 \; Moreover\, the conditional probabilities of the first marginal on these
  sets are absolutely continuous with respect to the k-dimensional Hausdorf
 f measure on the k-dimensional sets on which they are concentrated\, thus 
 settling the longstanding Sudakov's problem of the existence of locally af
 fine decompositions of <b>R</b><sup>d</sup> that reduce norm cost transpor
 tation problem to families of lower dimensional ones. Finally\, due to the
  minimality of our partition with respect to this &quot\;dimensional reduc
 tion&quot\; property\, applications to secondary cost functions obtained f
 irst minimizing with respect to a convex norm and then with respect to a f
 iner one (e.g.\, a strictly convex one) will be shown. These results were 
 obtained in collaboration with&nbsp\; Stefano Bianchini (SISSA\, Trieste).
DTEND;TZID=Europe/Zurich:20120328T161500
END:VEVENT
END:VCALENDAR