[PAST EVENT] Mathematics Colloquium: Charles Johnson (William & Mary)
Title: Eigenvalues, Multiplicities and Graphs
Abstract: This will be an introduction to how the graph (of a real symmetric matrix, or a general matrix) constrains the multiplicities of its eigenvalues. The case of trees is most interesting and this will be described in some detail, including the maximum multiplicity, the minimum number of distinct eigenvalues, the possible lists of multiplicities and how they come about. This talk will be an overview of the subject and a second talk in the GAG seminar will continue the description. The subject has just been covered in a new book from Cambridge University Press (same title), and REU students have helped to make some very important contributions over the years. There is still plenty of work to be done in the area, which has been of interest to algebraic graph theorists and numerical analysts, as well as matrix theorists.