ABSTRACT:
Pattern formation is one of the most studied aspects of animal communities. Some of the most striking patterns observed in these communities are related to the behaviour displayed by animal groups: from migrating herds of ungulates, to zigzagging flocks of birds, or the rippling waves of Myxobacteria. Understanding the biological and mathematical mechanisms behind the formation of these patterns, as well as the abrupt transitions between these patterns, has become an active area of research. In this talk, I will present and investigate a class of nonlocal hyperbolic models introduced to describe the formation and movement of self-organized biological aggregations. After a brief discussion of the models, I will focus on the large variety of spatial and spatiotemporal patterns displayed by these models, and discuss the mathematical approaches taken to investigate them. I will conclude by presenting some open problems related to the mathematical mechanisms behind some of the more complex patterns.
ADDITIONAL INFORMATION:
My research covers two main areas: (a) biological aggregations, with a focus on the formation, structure, and movement of these aggregations; (b) cancer immunotherapies.
During my PhD at University of Alberta, I proposed a general modelling framework to understand the multitude of aggregation patterns observed in biological aggregations. For this work, in 2009 I was awarded (by the Canadian Applied and Industry Mathematics Society (CAIMS)) the “Cecil Graham Doctoral Dissertation Award”.
As a postdoctoral fellow at McMaster University, I collaborated with both immunologists and mathematicians to model and identify the biological mechanisms behind the interactions among immune cells, cancer cells and viruses, with the purpose of improving existent cancer immunotherapies. In November 2011, I was awarded a “MITACS Postdoctoral Research Projects – Strategic Project Award” to mathematically identify and investigate cancer biomarkers that could be used to improve the effectiveness of oncolytic therapies for skin cancer.
