University of Victoria

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...

The arboricity \Gamma(G) of an undirected graph G = (V,E) is the minimal number such that E can be partitioned into \Gamma(G) forests. Nash-Williams' formula states that \Gamma(G) = \ceil{ \gamma(G) }, where \gamma(G) is the maximum of |E_H|/(|V_H|-1...

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...

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...

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...

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...

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...

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...