University of Victoria

In defining colouring of oriented graphs via homomorphism one finds an easily checkable necessary condition for a valid colouring — vertices at directed distance at most two must receive different colours. With this idea in mind we extend the...

The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G has “not too many small cutsets”. Severo, Tassion, and I have recently proved the converse. Our argument is inspired by an...

Let $G$ be a graph with $n$ vertices. Let $A(G)$ be its adjacency matrix. Let $\lambda_1(G), \lambda_2(G)$ denote the largest and second largest eigenvalues of the adjacency matrix. Bollob\'{a}s and Nikiforov (2007) conjectured that for any graph $G...

The notions of noise sensitivity and stability were recently extended for the voter model, a well-known and studied interactive particle system. In this model, vertices of a graph have opinions that are updated by uniformly selecting edges. We...

I will present a coupling between a massive planar Gaussian free field (GFF) and a random curve in which the curve can be interpreted as the level of the field. This coupling is constructed by reweighting the law of the standard GFF-SLE_4 coupling. I...

Spin glasses are disordered statistical physics system with both ferromagnetic and anti-ferromagnetic spin interactions. The Gibbs measure belongs to the exponential family with parameters, such as inverse temperature $\beta>0$ and external field $h...

An edge mapping of a graph is a function f:E(G) -> E(G) where f(e) \neq e for all e in E(G). A subgraph H of G is called f-free if for every e in E(H) f(e) \notin E(H). A graph G is called unavoidable for a graph H if every edge mapping of G has at...

A network of interacting qubits (usually subatomic particles) can be modelled by a connected weighted undirected graph $G$. The vertices and edges of $G$ represent the qubits and their interactions in the network, respectively. Quantum mechanics...

In the talk exchangeability appears in two different meanings. In the first part, the determination of the phase diagram of the Curie-Weiss model relies on De Finetti’s Theorem. The Curie-Weiss distribution will be expressed as a random mixture of...

Double dimers are superimposition of two perfect matchings. Such superimpositions can be decomposed into disjoint simple loops. The question we address is: as the graphs become large, in a 'typical' double dimer sample, do some of the loops diverge...