University of Manitoba

We are in the midst of an exciting revolution in quantum science and technology, comparable in ways to the first one that occurred about 100 years ago. One of the most tantalizing and potentially disruptive innovations to emerge from this second...

The spectral properties of matrices with prescribed patterns have received significant attention in recent research. This talk examines symmetric matrices that share the off-diagonal zero-nonzero pattern with the adjacency matrix of a given graph...

It is known that non-isomorphic strongly regular graphs with the same parameters must be cospectral (have the same eigenvalues). We investigate whether the spectra of higher order Laplacians associated with these graphs can distinguish them. In this...

There has been extensive study of diagonalization of matrices. Diagonalization can be viewed as using a similarity transform to concentrate the magnitude of all entries within as small a subset of entries as possible. We motivate and present results...

In this talk, we will introduce the Weak and the Strong Lefschetz Properties (WLP and SLP) focusing on Artinian complete intersections. A famous result of Stanley shows that every Artinian monomial complete intersection over a field of characteristic...

Let G = (V, E) be a simple graph of order n. The adjacency matrix of G is denoted by A(G) = [a_ij], where a_ij=1 if {v_i ,v_j} ∈ E and a_ij=0, otherwise. The diagonal matrix of degrees of G, D(G) = [d_ij], is defined by d_ii=d(v_i), and d_ij=0, ∀ i...

Let us ask: What is a "strong" matrix property and why is such a property useful for studying eigenvalues of graphs? During this talk we will attempt to address both questions above by first wandering through some of the developed strong matrix...

Let M be a Hermitian matrix associated to a graph X on n vertices. For any time t \geq 0, the transition matrix of the continuous quantum walk on X relative to M at time t is given by U(t)=exp(itM). For two vertices a and b of X, if there is some...

The signs of the entries of a real matrix can give insight into the eigenvalues of the matrix. A well-known example is the Perron Frobenius theorem for matrices that have no negative entries. As an inverse eigenvalue problem, one can ask for the...

For a fixed $d \in \mathbb{N}$, the non-commutative (nc) universe $\mathbb{M}^d$ is defined as the graded (disjoint) union of $d$-tuples of $n \times n$ (complex) matrices over $n \in \mathbb{N}$. A function $f : \mathbb{M}^d \to \mathbb{M}^1$ is...