Abstract: We consider the open problem of characterizing the set of all possible complex numbers that can be the eigenvalue of an n by n doubly stochastic matrix. We look at the solution of the corresponding problem for stochastic matrices by Karpelevich and interpret this solution in terms of partial orders. We then look at possible partial order approaches to the doubly stochastic problem motivated by the connection between doubly stochastic matrices and the majorization order. Some related results in quantum information theory and possible connections to group representations are also discussed. ------------- Zoom Link:https://westernuniversity.zoom.us/j/92796051710 Password:colloq