University of Manitoba

In this seminar we recall the spectral partitioning method based on a Fiedler vector, i.e., an eigenvector corresponding to the second smallest eigenvalue of the Laplacian matrix of a graph. This problem corresponds to the minimization of a quadratic...

There has been extensive study of diagonalization of matrices, or finding the Jordan Canonical Form for a matrix that is not diagonalizable. Diagonalization can be viewed as using a similarity to concentrate the magnitude of all the entries with a...

Zero forcing is a type of graph propagation based on the color-change rule: Given graph $G$, if each vertex of $G$ is colored either white or blue, and vertex $v$ is a blue vertex with only one white neighbor $w$, then change the color of $w$ to blue...

The UManitoba student chapter of the Association for Women in Mathematics (AWM) will be hosting a symposium on November 16, 2023. This hybrid symposium will take place in Armes 205 at the University of Manitoba Fort Garry campus in Winnipeg, Manitoba...

Given a connected undirected graph G = (V,E), where V is the set of vertices and E the set of edges (possibly with weights), denote by A the associated adjacency matrix. The Kemeny constant of the graph G is defined as the Kemeny constant of the...

Kemeny's constant, a fundamental parameter in the theory of Markov chains, has recently received significant attention within the graph theory community. Originally defined for a discrete, finite, time-homogeneous, and irreducible Markov chain based...

In this talk, I will discuss certain extremal configurations in Q-polynomial distance-regular graphs (or P- and Q-polynomial association schemes), which we call descendents. The descendents of a hypercube are precisely its faces. I will show how they...

Biological systems often give rise to systems of first order ordinary differential equations (ODEs). Linearization then yields a system x' = Ax, where A is the community matrix. By contrast, mechanical systems often give rise to a second order ODE...

We often encounter matrices whose pattern (zero-nonzero, or sign) is known while the precise value of each entry is not clear. Thus, a natural question is what we can say about the spectral property of matrices of a given pattern. When the matrix is...

After a review of n-by-n permutation matrices and n-by-n alternating sign matrices (ASMs), and their relationship, we will discuss the cones that they generate and their Hilbert Bases.