University of Alberta

Drug overdose deaths continue to increase in the United States, reaching a record of more than 100,000 deaths in 2021, driven mostly by fentanyl and methamphetamines. We propose a mathematical framework to describe the neurobiology of drug addiction...

Microplastics pose a severe threat to marine ecosystems; however, relevant mathematical modeling and analysis are lacking. This paper formulates two stoichiometric producer-grazer models to investigate the interactive effects of microplastics...

The question of how roots of polynomials move under differentiation is classical. Contributions to this subject have been made by Gauss, Lucas, Marcel Riesz, Polya and many others. In 2018, Stefan Steinerberger derived formally a PDE that should...

Quadratic form theory started as a part of number theory; people were notably interested in representation questions, such as which number of a given field can be written as a sum of a certain number of squares. In the 1930’s, Witt started the...

Cancer is a complex disease with many unknown features. The evolution of tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. To overcome some of the outstanding...

The Game of Cycles, introduced in my book Mathematics for Human Flourishing, is played on a connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a...

In this talk, I will introduce an SIS patch endemic model with cognitive dispersal. When $\mathcal{R}_0>1$, I give a sufficient condition for the uniqueness of endemic equilibrium. At the unique endemic equilibrium, I prove that the disease...

Malignant gliomas are highly invasive brain tumors. Recent attention has focused on their capacity for network-driven invasion, whereby mitotic events can be followed by the migration of nuclei along long thin cellular protrusions, termed tumour...

The data association problem is the difficult part of the multi-object tracking problem. The problem is to: (i) classify measurements (e.g., position, shape, etc) as true positives or false positives, ( ii) classify tracked objects as observed (i.e...

A revolution has been underway in wave physics in recent years based around concepts of resonance and microstructured media often coupled with periodicity. This has resulted in materials known as metamaterials that have, for instance, negative...