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DESCRIPTION: Convexity for the max-plus algebra has been studied from diffe
 rent directions including discrete geometry\, scheduling\, computational co
 mplexity. As there is no inverse for the max-operation\, this used to rely 
 on an implicit non-negativity assumption. We remove this restriction by int
 roducing `signed tropical convexity'. This allows to exhibit new phenomena 
 at the interplay between computational complexity and geometry. We obtain s
 everal structural theorems including a new Farkas lemma and a Minkowski-Wey
 l theorem for polytopes over the signed tropical numbers. Our notion has se
 veral natural formulations in terms of balance relations\, polytopes over P
 uiseux series and hyperoperations. 
DTSTAMP:20191031T213500
DTSTART:20191125T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9 
 \n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Georg Loho (London School of Economics and Political Science): Sign
 ed tropical convexity
UID:102526182@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20191125-L-Loh
 o.html
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