Algebraic Graph Theory Seminar

Title: Periodicity on Oriented Graphs by way of Transcendental Number Theory

Abstract: Using the adjacency matrix of a graph, it is straightforward to show that perfect state transfer between two vertices at some time t implies that both vertices will be periodic at time 2t. However,  when we consider a graph where each edge is oriented, this proof fails. All is not lost, though, and by using the Gelfond-Schneider theorem, we are able to prove that perfect state transfer implies periodicity. In this talk, we will give an overview of Gelfond-Schneider Theorem and its use in studying quantum walks.