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UID:5c8a5b8a6daef647601088@ist.ac.at
DTSTART:20190904T130000
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DESCRIPTION:Speaker: Sergey AVVAKUMOV\nhosted by Uli Wagner\nAbstract: Cons
 ider an abstract resource $X$ and $n$ players who want to divide it among 
 themselves.For each possible division of $X$ each player has their favorit
 e piece(s).The logic which the players use to choose the piece they like m
 ay be arbitrary complicated.Can we always find an envy-free division\, i.e
 .\, match players with pieces so that everyone gets a piece they like?Mode
 ling $X$ as a line segment and making some natural continuity assumption p
 lus an additional assumption that "something is better than nothing"\, i.e
 .\, that players never like an empty piece\, Gale (1984) provedthat an env
 y-free division exists for any $n$.Later it turned out that "something is 
 better than nothing" assumption is not necessarily essential. Without it\,
  Segal-Halevi (2018) and later Meunier and Zerbib (2018) proved that an en
 vy-free segment division exist for $n=3$ and $n=4$ or $n$ prime\, respecti
 vely.We prove that an envy-free segment division exist for $n$ prime power
 . For every $n$ not a prime power we construct an example where no envy-fr
 ee division is possible. This completely solves the problem.We also discus
 s what happens if $X$ is not assumed to be a line segment.Joint work with 
 Roman Karasev.
LOCATION:Mondi Seminar Room 3\, Central Building\, ISTA
ORGANIZER:hwagner@ist.ac.at
SUMMARY:Sergey AVVAKUMOV: GeomTop Seminar: Envy-free division and degrees o
 f equivariant maps.
URL:https://talks-calendar.ista.ac.at/events/2088
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