University of Victoria

Bounded density shifts are examples of hereditary subshifts. Bounded density shifts are defined by disallowing words whose sum of entries exceeds a value depending on the length of the word. After presenting some examples and reviewing the concepts...

Recent interactions between probability and number theory proved fruitful. In particular, random multiplicative functions (RMFs) are random models for partial sums of the Möbius function and Dirichlet characters, which are related to L-functions like...

In how many ways can an m x n chessboard be tiled using 2 x 1 tiles? The solution is given by the number of perfect matchings in a related graph. Although computationally difficult in general, in this circumstance we are able to efficiently count...

An (m, n)-mixed graph consists of a set of vertices, any two of which may be joined by either an edge of one of m colours or an arc of one of n colours, or not be joined at all. The operation of switching at a vertex v of an (m, n)-mixed graph with...

Comparative genomics offers valuable insights into evolutionary biology, uncovering patterns such as whole-genome duplications, gene retention, and gene loss. Polyploidization, a widespread evolutionary process, plays a pivotal role in shaping the...

Particle Swarm Optimization (PSO) algorithm is based on swarm intelligence and widely used in the field of Artificial Intelligence. Like many other nature-inspired metaheuristic algorithms, it is already widely used to tackle all sorts of hard...

This talk will present a novel discretization scheme for Wasserstein gradient flows (i.e. curves of steepest descent for functions of probability measures) based on the successive computation of Schrödinger bridges with equal marginals. In doing so...

In defining colouring of oriented graphs via homomorphism one finds an easily checkable necessary condition for a valid colouring — vertices at directed distance at most two must receive different colours. With this idea in mind we extend the...

Many fundamental problems in extremal combinatorics can be expressed as inequalities in graph homomorphism densities. In this talk, I will introduce some new results on this topic. Our research involves Sidorenko's conjecture, Kohayakawa-Nagle-R{\"o...

The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G has “not too many small cutsets”. Severo, Tassion, and I have recently proved the converse. Our argument is inspired by an...