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SUMMARY:Symmetrically coloured Gaussian graphical models with toric vanish
 ing ideals - Jane Coons (University of Oxford)
DTSTART:20240124T114500Z
DTEND:20240124T124500Z
UID:TALK208063@talks.cam.ac.uk
DESCRIPTION:Gaussian graphical models are multivariate Gaussian statistica
 l models in which a graph encodes conditional independence relations among
  the random variables. Adding colors to this graph allows us to describe s
 ituations where some entries in the concentration matrices in the model ar
 e assumed to be equal. In this talk\, we focus on RCOP models\, in which t
 his coloring is obtained from the orbits of a subgroup of the automorphism
  group of the underlying graph. We show that when the underlying block gra
 ph is a one-clique-sum of complete graphs\, the Zariski closure of the set
  of concentration matrices of an RCOP model on this graph is a toric varie
 ty. We also give a Markov basis for the vanishing ideal of this variety in
  these cases. Finally\, we present preliminary results on the ideals of RC
 OP graphs which are not block graphs. This is joint work with Aida Maraj\,
  Pratik Misra and Miruna-Stefana Sorea.
LOCATION:Seminar Room 1\, Newton Institute
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