University of Victoria

The homomorphism density of a graph H in a graph G is the probability that a random function from the vertex set of H to the vertex set of G is a graph homomorphism. A natural question studied by Leontovich and Sidorenko back in the 80s and 90s is...

Structural Ramsey theory generalizes classical Ramsey theory by considering classes of finite sets with additional structure (such as finite groups or finite partial orders) and colourings of their substructures. When the class satisfies an...

Given a graph H, say that a graph G is properly rainbow H-saturated if there exists a rainbow H-free proper edge-colouring of G and, for any non-edge e of G, every proper edge-colouring of G+e contains a rainbow copy of H. The proper rainbow...

Fairness in machine learning classification has been a topic of great interest given the increasing use of such classifiers in critical settings. There are many possible definitions of fairness and many potential sources of unfairness. Given this...

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...

I'll begin by describing shifts of finite: topological dynamical systems based on some simple combinatorial data. These have played a fundamental role in hyperbolic dynamics. I will then describe a new construction of factors (quotients) of such...

Schrödinger operators with delta potentials are of longstanding interest for admitting solutions expressible in closed analytic forms. By some duality, these operators also receive new interest for solving moments of the continuum directed random...

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...

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...

In 1975, the physicists Imry and Ma predicted that the incorporation of a random field in low-dimensional spin systems leads to the rounding of first-order phase transitions. These predictions were rigorously established by Aizenman and Wehr in 1989...