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...

Take an Ising model with very low temperature. What is the largest p such that the Ising model dominates Bernoulli percolation with parameter p ? We will show that the answer to this question depends drastically on the geometry of the graph. We also...

The Perceptron model was proposed as early as the 1950's as a toy model of a one-layer neural network. The basic model consists of a set of solutions (either the Hamming cube or the sphere of dimension n) and a set of constraints given by independent...

I will describe the large-scale behavior of a random growth model (Internal DLA) on random planar maps which approximate a random fractal surface embedded in the plane (Liouville quantum gravity, LQG). No prior knowledge of these objects will be...

Random projections of high-dimensional probability measures have gained much attention in asymptotic convex geometry and high-dimensional statistics. While fluctuations at the level of the central limit theorem have been classically studied, only...

How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality...

If a tricky devil challenged you to complete a Sudoku puzzle of their design, what restrictions could you place on their design to guarantee it was impossible for them to thwart your attempts? More specifically, if you could dictate exactly how many...

An $(m,n)$-generalized bent function is a function from $\mathbb{Z}_2^n$ to $\mathbb{Z}_m$ so that its associated Fourier transformations have constant absolute value. It is known that an $(m,n)$-generalized bent function exists whenever one of the...

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...