University of Victoria

We will discuss extensions of random transpositions to other conjugacy classes. Our main probabilistic result is the total variation cutoff profile for these random walks, under a mild assumption on the number of fixed points. The proof is based on a...

Although biologists discover and classify thousands of new species each year, an estimated 95% of the more than 20 million multicellular species on Earth remain unnamed and unclassified. Our research aligns with the long-term goals of the Planetary...

We consider the model in which uniform random points are added to the unit interval at a constant intensity and independently vanish each at rate 1. The stationary distribution is a Poisson point process. Our goal is to investigate the time until an...

A sequence of tournaments is said to be quasirandom if it behaves as a sequence of random tournaments would. In 1991, Chung, Graham, and Wilson provided a list of equivalent properties that any sequence of random tournaments satisfies with high...

There is now an expansive collection of mathematical work on building models for the transport of intracellular cargo by molecular motors. Commonly studied cargo undergo “saltatory” motion (bidirectional ballistic motion, intermixed with periods of...

The mixing time and spectral gap of a random walk on the symmetric group can sometimes be understood in terms of its low dimensional representations (e.g., Aldous' spectral gap conjecture). It turns out that under a mild degree condition involving...

Algebraic graph theory begins by associating a matrix to a graph and asking how the eigenvalues of the former relate to the structure of the latter. In the past fifteen or so years, horizons have broadened to include variants of graphs (such as...

The peaceable queens problem asks to determine the maximum number $a(n)$ such that there is a placement of $a(n)$ white queens and $a(n)$ black queens on an $n \times n$ chessboard so that no queen can capture any queen of the opposite color. We...

A phase transition is a phenomenon in physics, chemistry, and other related fields where the macroscopic behavior of a system changes qualitatively when the tuning parameter (such as temperature) that governs local interactions is varied by a small...

School timetabling is a complex problem in combinatorial optimization, requiring the best possible assignment of course sections to teachers, timeslots, and classrooms. For educational institutions, the Master Timetable dictates to every single...