University of Victoria

Eternal domination is a graph game where mobile guards are placed on vertices and then moved in order to defend against sequences of attacks. If only one guard is allowed to move in response to an attack, then it has been shown that there is no...

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...

We study a mean-field spin glass model whose coupling distribution has a power-law tail with exponent \alpha \in (0, 2). This is known as Levy spin glasses in literature. Though it is a fully connected model, many of its important characteristics are...

The random interlacement point process (introduced by Sznitman, generalized by Teixeira) is a Poisson point process on the space of labeled doubly infinite nearest neighbour trajectories modulo time-shift on a transient graph G. We show that the...

In this talk I will be speaking about the dimer model sampled on a general Riemann surface. Dimer model on a graph consists of sampling a random perfect matching with the probability proportional to the product of edge weights. In the case when the...

The GFF is localised on trees because the random walk is transient. What about other height functions? We present rigorous localisation results for two other height functions using elementary methods.

In life history studies one often encounters situations where individuals in a population are eligible to enroll only if the response time does not exceed an associated censoring time, which leads to the so called left truncated lifetime data. While...

The Liouville quantum gravity (LQG) surface, formally defined as a 2-dimensional Riemannian manifold with conformal factor being the exponentiation of a Gaussian free field, is closely related to random planar geometry as well as scaling limits of...

A broad class of problems in extremal geometry can be characterized as follows. Fix a positive integer k and a property of k-tuples of points in R^2. The problem is then to determine how many k-tuples in an n-point set in R^2 can have the chosen...

A Latin square is an n by n grid filled with n symbols so that each symbol appears exactly once in every row and column. A transversal in a Latin square is a selection of entries with no row, column, or symbol repetition. The study of transversals in...