University of Victoria

Probabilistic zero-forcing can be thought of as a model for rumour spreading, where a person is more likely to spread a rumour if several of their friends already believe it. We start with a graph that has one infected vertex. At each time step an...

The Manickam-Miklós-Singhi Conjecture states that for positive integers n and k with n > (4k - 1), a multi-set X = {x_1,x_2, … ,x_n} with real entries and nonnegative sum has at least \binom{n-1}{k-1} subsets of size k with nonnegative sum. This talk...

A momentous legacy of twentieth-century mathematics is the realisation that deterministically evolving systems frequently exhibit, when observed for sufficiently extended periods of time, a statistical behaviour akin to the limiting behaviour of...

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...

How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality...

It is common in probability theory and statistics to study distributional convergences of sums of random variables conditioned on another such sum. In this talk I will present a novel approach using Stein’s method for exchangeable pairs that allows...