Graduate Computational Algebraic Geometry Seminar
Elizabeth Gross
UIC
Markov complexity of hypergraphs
Abstract: The toric ideal of an edge subring of a graph is an object that
appears when studying statistical models parameterized by the edges of a
graph. There are many results that tell us the same beautiful story: we can
understand these ideals if we understand the combinatorics of the underlying
graph. A natural extension is to consider the defining ideal of an edge
subring of a hypergraph. In this talk we give some recent results on the
toric ideals of hypergraphs, including how to tell if the ideal is generated
in a fixed degree. The proposed construction provides the basic step for
understanding the combinatorial complexity of these generators, which, in
algebraic statistics, provide a Markov basis for the underlying statistical
model. This is joint work in progress with Sonja Petrovic.
Thursday March 15, 2012 at 11:00 AM in SEO 1227