Date: Friday, October 08, 2021
Location: Online (1:00 PM to 2:00 PM)
Title: Asymptotic Behaviours of Hierarchical Models
Abstract: The algebraic objects in this talk are motivated by applications to algebraic statistics. Toric ideals of hierarchical models are invariant under the action of a product of symmetric groups. Taking the number of factors, say m, into account we introduce and study invariant filtrations and their equivariant Hilbert series. We present a condition that guarantees that the equivariant Hilbert series is a rational function in m+1 variables with rational coefficients. Furthermore we give explicit formulas for the rational functions with coefficients in a number field and an algorithm for determining the rational functions with rational coefficients. A key is to construct finite automata that recognize languages corresponding to invariant filtrations. Lastly, the method provided in this work allows one to define Segre languages of algebraic objects in a more general framework. This is based on joint work with Uwe Nagel.
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Speaker: Aida Maraj
Institution: UM
Event Organizer: Andrew Snowden asnowden@umich.edu
