Title: The non-backtracking matrix
| Speaker: | Carolyn Reinhart |
| Affiliation: | Swarthmore College |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: A non-backtracking walk in a graph is any traversal of the vertices of a graph such that no edge is immediately repeated. The non-backtracking matrix of a graph is indexed by the directed edges of the graph, and encodes if two edges can be traversed in succession. Since this matrix is not symmetric, the question of when the matrix is diagonalizable is of interest to those who study it. Equivalently, such graphs have a non-trivial Jordan block. In this talk, I will present an overview of the non-backtracking matrix, including its history and applications. Finally, I will present recent results about graphs with non-trivial Jordan blocks for the non-backtracking matrix from joint work with Kristin Heysse, Kate Lorenzen, and Xinyu Wu.