University of Alberta

Cells must reliably coordinate responses to noisy external stimuli for proper functionality. In this talk I will present a perspective on this important problem via extreme statistics. The central premise is that when a single stochastic process...

Given a convex solid in 3D space, how many light sources do we have to place around it in order to illuminate its entire surface? What is the minimum number that works? We call this number the illumination number of the solid, and perhaps a bit...

A hybrid asymptotic-numerical approach is developed to study hotspot patterns for a three-component 1-D reaction-diffusion (RD) system that models urban crime with police intervention. Our analysis is focused on a scaling regime where there are two...

We study a single-period optimal transport problem with a cost function given by a general bilinear form and a backward martingale constraint. The role of Kantorovich potentials is played by Fitzpatrick functions. The dual problem is a pseudo...

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...

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...

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...