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VERSION:2.0
PRODID:-//Memento EPFL//
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SUMMARY:A fractal Optimal Shape in Branched Transport
DTSTART:20190301T140000
DTEND:20190301T150000
DTSTAMP:20260924T071708Z
UID:0a6b1fa429a2d20160818151b0f5ead0311ed5bb937a8184f16b48bd
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Paul PEGON\nThe branched transport problem consists in con
 necting two measures of same mass through a network minimizing a certain c
 ost. Typically if a mass m moves over a distance L\, it is of the form m L
 ^α where α is an exponent between 0 and 1. I will shortly introduce the 
 theory of branched transport and the so-called landscape function\, essent
 ial to the study of related variational problems. I will then address the 
 following question: what is the set of unit volume which can be best irrig
 ated starting from a single source at the origin\, in the sense of branche
 d transport? We formulate this question as a shape optimization problem wh
 ose solutions may be thought as ``unit balls" for branched transport. Our 
 main motivation for considering this problem is to exhibit fractal feature
 s of branched transport\, the boundary of such balls being natural candida
 tes. Indeed\, we are able to get an upper bound on the Minkowski dimension
  of the boundary\, which is non-integer and conjectured to be its exact di
 mension. I will finally present a first attempt to compute numerically an 
 approximate optimal shape\, using a Modica-Mortola approximation of branch
 ed transport introduced some years ago by Oudet and Santambrogio. This is 
 a joint work with F. Santambrogio and Q. Xia.\n\n 
LOCATION:MA B1 11 https://plan.epfl.ch/?room=MAB111
STATUS:CONFIRMED
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