Title: Eigenvalues for stochastic matrices with a prescribed stationary distributionSpeaker: Steve Kirkland Affiliation: University of Manitoba Location: Please contact Sabrina Lato for Zoom link
Abstract: A square nonnegative matrix T is called stochastic if all of its row sums are equal to 1. Under mild conditions, it turns out that there is a positive row vector w^T (called the stationary distribution for T) whose entries sum to 1 such that the powers of T converge to the outer product of w^T with the all-ones vector. Further, the nature of that convergence is governed by the eigenvalues of T.
In this talk we explore how the stationary distribution for a stochastic matrix exerts an influence on the corresponding eigenvalues.
Title: Bounding the extended complexity of the stable set polytope on perfect graphsSpeaker: Gabriel Morete Affiliation: University of Waterloo Room: MC 6029
Abstract: This week we will study the extension complexity of the stable set polytope for perfect graphs. More than 40 years ago, Grötschel et al. gave an algorithm to find maximal weight stable sets on perfect graphs based on a compact semidefinite extension. However, whether there is a compact linear extension is still an open problem.
Title: Chromatic Symmetric Functions: Combining Algebra and Graph TheorySpeaker: Logan Crew Affiliation: University of Waterloo Room: MC 5479
Abstract: The chromatic polynomial, enumerating the proper colorings of a graph by number of colors used, was created by Birkhoff in the early 1900s to study the then Four-Color Conjecture. In the 1990s, Stanley generalized this to a chromatic symmetric function, which further counts for each proper n-coloring how many times each of the n colors is used.