Dr. Morgan Craig is a Researcher at the Sainte-Justine University Hospital Research Centre and an Assistant Professor in the Department of Mathematics and Statistics at the Université de Montréal. She was a postdoc in the Department of Organismic and Evolutionary Biology at Harvard University working with Dr. Alison Hill after receiving her Ph.D. in Pharmaceutical Sciences from the Université de Montréal. The Quantitative and Translational Medicine Laboratory that she runs focuses on the application and implementation of quantitative approaches, particularly computational biology, to study how heterogeneity impacts on disease and treatment outcomes. Her research focuses on the development of predictive, mechanistic models in a variety of disease contexts, particularly cancers and diseases caused by viruses, to identify pathophysiological mechanisms and tailor therapeutic regimens according to patient-specific characteristics. Dr. Craig’s research is highly multidisciplinary and is conducted in close collaboration with experimentalists and clinicians.

My research interests are around dynamical systems in small dimension, either ODE or difference equations.

In the case of ODE, I am interested in the qualitative theory of ODE and the development of methods allowing understanding the geometric organization of the solutions, often summarized in the phase portrait. I am especially interested to parameter dependent ODE and bifurcation analysis: bifurcations correspond to qualitative changes on the phase portraits occurring for particular values of the parameters. I am interested in applications to Hilbert 19s 16th problem on one side and, occasionally, to some predator-prey models in mathematical biology.

The main part of my recent research deals with the study of equilibrium positions of analytic dynamical systems depending on parameters, more precisely with the problem
of analytic classification of singularities of families of dynamical systems depending on parameters: when are two analytic families of dynamical systems equivalent modulo an analytic change of parameters and possibly a reparameterization of time? There are many obstructions to such equivalences and I am interesting in understanding their geometric meaning.

I am also very involved in popularization of mathematics and the training of future high school teachers.
I was the instigator and international coordinator of the international year Mathematics of Planet Earth 2013 (MPE2013).