Totally positive matrices, those whose minors are all positive, have been studied extensively in various branches of mathematics, including discrete math, probability, analysis and differential equations, interpolation theory and splines, and representation theory. Toeplitz and Hessenberg matrices have each similarly maintained a long and well-worn history of applications and theory. We are interested in studying an ensemble of matrices that lie at the intersection of these three matrix forms. Using numerical and theoretical approaches, we establish new spectral and structural properties for these hybrid models. This work is joint with Nick Ercolani and Jon Ramalheria-Tsu.

Zoom link: https://arizona.zoom.us/j/81196695512