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SUMMARY:Aida Maraj (University of Kentucky)
DTSTART:20200421T162000Z
DTEND:20200421T165000Z
DTSTAMP:20260423T004820Z
UID:NASO/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NASO/9/">The
  Equivariant Hilbert Series of Hierarchical Models</a>\nby Aida Maraj (Uni
 versity of Kentucky) as part of Max Planck Institute nonlinear algebra sem
 inar online\n\n\nAbstract\nA hierarchical model is realizable by a simplic
 ial complex that describes the dependency relationships among random varia
 bles and the number of states of each random variable. Diaconis and Sturmf
 els have constructed toric ideals that provide useful information about th
 e model. This talk concerns quantitative properties for families of ideals
  arising from hierarchical models with the same dependency relations and v
 arying number of states. We introduce and study invariant filtrations of s
 uch ideals\, and their equivariant Hilbert series. A condition that guaran
 tees this multivariate series is a rational function will be presented. Th
 e key is to construct finite automata that recognize languages correspondi
 ng to invariant filtrations. Lastly\, we show that one can similarly prove
  the rationality of an equivariant Hilbert series for some filtrations of 
 algebras. This is joint work with Uwe Nagel.\n
LOCATION:https://researchseminars.org/talk/NASO/9/
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