University of Victoria

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...

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...

The arboricity \Gamma(G) of an undirected graph G = (V,E) is the minimal number such that E can be partitioned into \Gamma(G) forests. Nash-Williams' formula states that \Gamma(G) = \ceil{ \gamma(G) }, where \gamma(G) is the maximum of |E_H|/(|V_H|-1...

Many systems whose physics is generally well understood are modeled with differential equations. However, many of these differential equations have the property that they are sensitive to the choice of initial conditions. If one instead has snapshots...

I will introduce the Monomer-Dimer model, a Gibbs probability measure on the space of (not necessarily perfect) weighted matchings on a graph. I will recap some known results of Heilmann and Lieb which establish the absence of a phase transition. I...

For graphs $G, H_1,\dots,H_r$, write $G \to (H_1, \ldots, H_r)$ to denote the property that whenever we $r$-colour the edges of $G$, there is a monochromatic copy of $H_i$ in colour $i$ for some $i \in \{1,\dots,r\}$. Mousset, Nenadov and Samotij...

For a simple graph $G$ on $n$ vertices, let $\mathcal{S}(G)$ be the set of all $n\times n$ real symmetric matrices $A=[a_{i,j}]$ with $a_{i,j}\neq 0$ if and only if $\{i,j\}$ is an edge of $G$. There are no restrictions on the diagonal entries of $A$...

In 1954, Tutte made a conjecture that every graph without a cut-edge has a nowhere-zero 5-flow. A parallel conjecture to this, but for signed graphs is Bouchet’s Conjecture (1983) that every signed graph without the obvious obstruction has a nowhere...

In the eternal eviction game, a set of guards placed on the vertices of (a dominating set of) a graph G must move to defend the graph against attacks on those of its vertices that contain guards, while maintaining a dominating set of G. The eternal...

Math Mania is a math education event which presents a variety of interactive demonstrations allowing students to learn math concepts in a fun and engaging way.