University of Victoria

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...

We show that \((n,d,\lambda)\)-graphs with \(\lambda=O(d/log^3n)\) are universal with respect to all bounded degree spanning trees. This significantly improves upon the previous best bound due to Han and Yang, and makes progress towards a problem of...

A combinatorial object is said to be quasirandom if it exhibits certain properties that are typically seen in a truly random object of the same kind. It is known that a permutation is quasirandom if and only if the pattern density of each of the...

A geometric graph $G$ is a graph $G$ whose vertices are drawn in the plane such that no three vertices are collinear, and each edge of G is a straight line segment. A geometric homomorphism from geometric graph $G$ to geometric graph $H$ is a...

Strong cocomparability graphs are the reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows 01, 10. Strong cocomparability graphs form a subclass of cocomparability...

The boxicity of a graph G is a key graph parameter introduced by Roberts in 1969. It represents the minimum dimension d such that G can be realized as the intersection graph of a family of axis-parallel boxes in R^d. Boxicity is an important measure...

Counting lattice paths with unit up and right steps beginning at the origin that are somehow constrained by a boundary is an old problem. When the boundary is the line y=x the celebrated Chung-Feller theorem states the number of paths having k flaws...

We analyse the metastable behaviour of the disordered Curie-Weiss-Potts (DCWP) model subject to a Glauber dynamics. The model is a randomly disordered version of the mean-field q-spin Potts model (CWP), where the interaction coefficients between...

The directed landscape is a random directed metric on the plane that arises as a scaling limit of a classical metric models in the KPZ universality class. In this talk, we will discuss a functional large deviation principle (LDP) for the entire...

A spanning tree of a finite connected graph G is a connected subgraph of G that includes every vertex and contains no cycles. In this talk we will consider uniformly drawn spanning trees of high-dimensional graphs, and explain why, under appropriate...