Rob Corless, Department of Applied Mathematics, Western University

The BOunded HEight Matrix of Integers Eigenvalue project, or "Bohemian Eigenvalue Project" for short, has its original source in the work of Peter Borwein and Loki Jorgenson on visible structures in number theory (c 1995), which did computational work on roots of polynomials of bounded height (following work of Littlewood). Some time in the late 90's I realized that because their companion matrices also had bounded height entries, such problems were equivalent to a subset of the Bohemian eigenvalue problems. That they are a proper subset follows from the Mandelbrot matrices, which have elements {-1, 0} but whose characteristic polynomials have coefficients that grow doubly exponentially, in the monomial basis. There are a great many families of Bohemian eigenvalues to explore: companion matrices in other bases such as the Lagrange basis (my work here dates to 2004), general Bohemian dense matrices, circulant and Toeplitz matrices, complex symmetric matrices, and many more. The conference poster contains an image from this project. This talk presents some of our recent results. Joint work with Steven Thornton, Sonia Gupta, Jonny Brino-Tarasoff, and Venkat Balasubramanian