Sabrina Lato, Department of Combinatorics & Optimization, University of Waterloo
"Perron, Frobenius, and some unexpected applications"
The Perron-Frobenius Theorem is a powerful theorem about non-negative matrices, with applications to algebraic graph theory, Markov chains, compact operators, as well as more practical applications in economics, demography, and Google's PageRank algorithm. However, the theorem itself was proved before any of those applications were known. The first formulation came out of Perron's work on continued fractions, adapted to positive matrices, and this was later expanded by Frobenius. In this talk, we'll explore the history and context of the Perron-Frobenius Theorem, as well as its application to graph spectra.