Colloquium: “Kirchoff Graphs: Existence, Construction, and Uniformity”

Date and time: Friday September 7, 2018 – 3:15 PM-4:15 PM

Location: Yost 306

Speaker: Professor Joseph D. Fehribach, WPI Mathematical Sciences

Abstract: Kirchhoff graphs are vector graphs which satisfy the Kirchhoff laws and can be used as circuit diagrams for chemical and other reaction networks. Construction of Kirchhoff graphs associated with a given matrix can be a difficult problem, and in general it is still an open question whether or not there exists a Kirchhoff graph for any matrix with rational entries. This talk discusses the existence of Kirchhoff graphs and a number of recent developments concerning their construction. These include a numerical algorithm for their construction based the rank and nullity of the matrix, and a explicit construction for rank 2, nullity 2 matrices over the rationals. We will also discuss which Kirchhoff graphs are uniform, meaning that they have a same total number of each edge vector.

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