University of Manitoba

Suppose Alice can send a quantum message to Bob in a quantum system modeled as a finite graph. But, imagine there is an eavesdropper which can attach an infinite-dimensional quantum system to the finite graph used by Alice and Bob. Can Alice still...

The eccentricity matrix ε(G) of a connected graph G is obtained from the distance matrix of G by keeping the largest nonzero entries in each row and each column, and leaving zeros in the remaining ones. The eigenvalues of ε(G) are the ε-eigenvalues...

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.

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 first review some known results about resistance matrix of an undirected graph. We then define resistance distance in a strongly connected, directed graph. When the graph is balanced, that is, the indegree and the outdegree of any vertex are the...

The adjacency matrix A of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. If u and v are distinct vertices in G, we say perfect state transfer from u to v occurs if there is a time t such that the (u,v)-entry of...

Let G be a simple connected graph and A(G) be its adjacency matrix. A nonsingular graph G is said to have the reciprocal eigenvalue property if the reciprocal of each eigenvalue of G is also an eigenvalue. Furthermore, if each eigenvalue of G and its...

Math Outreach: Many Needs, Many Ways I will present a wide range of math educational outreach activities involving elementary, middle and secondary level students. By expecting children to succeed, introducing new and exciting ways to teach...

Math Academy for incoming Indigenous Nursing Students. We will be working on basic skills to get them ready for their math course which starts in September.