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DESCRIPTION: A matroid  is a combinatorial object based on an abstraction o
 f linear independence in vector spaces and forests in graphs. It is a class
 ical question to determine whether a given matroid is representable as a ve
 ctor configuration over a field. Such a matroid is called linear.  This tal
 k is about a generalization of that question from vector configurations to 
 c-arrangements. A c-arrangement for a fixed c is an arrangement of dimensio
 n c subspaces such that the dimensions of their sums are multiples of c. Ma
 troids representable as c-arrangements are called multilinear matroids.  We
  prove that it is algorithmically undecidable whether there exists a c such
  that a given matroid has a c-arrangement representation. In the proof\, we
  introduce a non-commutative von Staudt construction to encode an instance 
 of the uniform word problem for finite groups in matroids of rank three.  T
 he talk is based on joint work with Geva Yashfe. 
DTSTAMP:20191202T145400
DTSTART:20200106T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9 
 \n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Lukas Kühne (Hebrew University of Jerusalem): Matroid representatio
 ns by c-arrangements are undecidable
UID:95692836@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20200106-C-Kue
 hne.html
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