University of Manitoba

The relationship between mapping class groups of surfaces and low-dimensional topology has long been a fruitful one. From Thurston's characterization of geometric structures on mapping tori in terms of the Nielsen-Thurston type of the mapping class...

When subjects are exposed to full field flicker in certain frequencies, they perceive a variety of complex geometric patterns that are often called flicker hallucinations. On the other had, when looking at high contrast geometric patterns like op art...

In meiosis, DNA is copied from parents to offspring, so that individuals who share common ancestors may have identical DNA copies from those ancestors through repeated meiosis. This identical-by-descent (IBD) DNA underlies the similarities between...

We develop a dynamic programming methodology that seeks to maximize investor outcomes over multiple, potentially competing goals (such as upgrading a home, paying college tuition, or maintaining an income stream in retirement), even when financial...

Dynamical systems concepts have mostly been developed to understand the behaviour of autonomous, i.e. input-free, nonlinear systems. Even in this case, it is well recognized that such systems can display a wide range of dynamical behaviours...

Non--isomorphic graphs with isomorphic canonical double cover (CDC) have the same number of walks of arbitrary length from corresponding vertices of the same degree. The total number of walks, for a specific length, depends only on the main...

An interesting question in spectral graph theory is about the structure of the eigenvectors of matrices associated with graphs. A graph is weakly Hadamard diagonalizable (WHD) if its Laplacian matrix L can be diagonalized with a weakly Hadamard...

For r ≥ 1, a graph has r-friendship property if every pair of vertices has exactly r common neighbours. The motivation for this definition is from the friendship theorem, which is on the graphs with 1-friendship property. The friendship theorem...

In this talk I will talk about some of my favorite problems which remain open in the field of continuous-time quantum walks in graphs.

Kemeny's constant is an interesting and useful quantifier of how well-connected the states of a Markov chain are. Though it was first introduced in the 1960s, interest in this concept has recently exploded. This talk will provide an introduction to...