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Talk: Entanglement for graph and higher-rank graph traces

2/21/17 4:15pm to 5:00pm

Math Colloquium

Dr. Danny Crytser

Kansas State

A trace on a directed graph is a real function on the vertices that satisfies certain equations coming from the adjacency relations. These traces are used to define interesting linear transformations on operator algebras, a sub-field of functional analysis. If you take the product of two graphs E and F, you obtain a new graph E x F, and the traces on E x F come in two flavors: those you can “factor” as a trace on E times a trace on F (call these product traces), and those you cannot (call these entangled traces). The language of entanglement comes from quantum mechanics. A related concept is that of an extreme trace, one which cannot be written as a weighted average of other traces. In this talk I’ll describe some results on graph traces an REU group under my supervision obtained during Summer 2016, as well as some conjectures I would like to see verified in the future.