University of Victoria

Much of the recent rigorous progress on the classical Ising model was driven by new detailed understanding of its stochastic geometric representations. Motivated by the problem of establishing exponential decay of truncated correlations of the...

Site percolation models are probability distributions of 2-colorings of the vertices of locally finite infinite graphs. Historically, they have been studied on graphs exhibiting symmetries such as (quasi)-transitivity. In joint work with Alexander...

We will introduce Random Spanning Trees in Random Environment (RSTRE), a disordered system on spanning trees that interpolates between the Uniform Spanning Tree (UST) and Minimum Spanning Tree (MST) measures. Our primary goal is to study how local...

Consider a random uniform sample of size $n$ over a bounded region $A$ in $R^d$, $d \geq 2$, having a smooth boundary. The coverage threshold $T_n$ is the smallest $r$ such that the union $Z$ of Euclidean balls of radius $r$ centred on the sample...

One of the main goals of statistical mechanics is to understand critical phenomena of lattice models. This can be achieved by computing the so-called critical exponents, which govern algebraic scaling near or at the critical point. This task is...

I will discuss several recent results on the Turán density of long cycle-like hypergraphs. These results (due to Kamčev–Letzter–Pokrovskiy, Balogh–Luo, and myself) all follow a similar framework, and I will outline a general strategy to prove Turán...

The Turan density of a forbidden hypergraph F is the largest edge density a large hypergraph H can have without containing any copy of F, and determining this number for various F is a notoriously difficult problem. One on-ramp to this question (from...

Spatial Pattern Formation and the Evolution of Cooperative Behaviour

A 2-cell embedding of a graph G in an orientable surface of genus k is an embedding in which each face is homeomorphic to an open disk. The distribution of genus across all 2-cell embeddings of G is called the genus distribution of G. In this talk...

The question of whether one graph can be embedded in another is a fundamental problem in graph theory. In 2020, Joos and Kim introduced a generalization of the basic graph embedding problem to graph collections. Let $G=\{G_1,\ldots,G_m\}$ be a...