University of Victoria

Reproductive value is the relative expected number of off-springs produced by an individual in its remaining lifetime. It is also an invariant function for population processes with birth and death rates independent of the time except in cases when...

In 2017, Ron Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture: if G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most the ceiling of n...

A collection of families $(\F_{1}, \F_{2} , \cdots , \F_{k}) \in \mathcal{P}([n])^k$ is \emph{cross-Sperner} if there is no pair $i \not= j$ for which some $F_i \in \F_i$ is comparable to some $F_j \in \F_j$. Two natural measures of the `size' of...

For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific...

Reproductive value is the relative expected number of off-springs produced by an individual in its remaining lifetime. It is also an invariant function for population processes with birth and death rates independent of the time except in cases when...

Take an Ising model with very low temperature. What is the largest p such that the Ising model dominates Bernoulli percolation with parameter p ? We will show that the answer to this question depends drastically on the geometry of the graph. We also...

Random projections of high-dimensional probability measures have gained much attention in asymptotic convex geometry and high-dimensional statistics. While fluctuations at the level of the central limit theorem have been classically studied, only...

The Perceptron model was proposed as early as the 1950's as a toy model of a one-layer neural network. The basic model consists of a set of solutions (either the Hamming cube or the sphere of dimension n) and a set of constraints given by independent...

I will describe the large-scale behavior of a random growth model (Internal DLA) on random planar maps which approximate a random fractal surface embedded in the plane (Liouville quantum gravity, LQG). No prior knowledge of these objects will be...

The Helly number of a set in the plane is the smallest N such that the following is true. If any N members of a finite family of convex sets contains a point of S, then there is a point of S which is contained in all members of the family. An...