Research

I am currently part of Dr. Hao Wang’s research group at the University of Alberta. You can find some information here. Our group has a wide range of research directions, such as stoichiometry based modelling efforts, microbiology, infectious disease modelling, habitat destruction & biodiversity, as well as spatial memory and cognition. My recent focus has been on modelling habitat loss (destruction, degradation & fragmentation) in a partial differential equation framework, as well as modelling animal movement with the inclusion of cognitive abilities, often absent from existing classical models.

My research interests lie primarily in the analysis and application of partial differential equations, or PDEs. On one hand, the analysis of PDEs is often a challenging and nuanced venture with a functionally infinite amount of existing results to learn and discover. On the other hand, the application of PDEs to real world phenomena can act as a focusing lens to motivate the analytical tools one might develop.

On the analysis side of PDEs, I have spent a portion of time studying the existence, regularity and long term behaviour of solutions to parabolic and elliptic equations and systems. On the application side of PDEs, I have spent a portion of time studying time dependent problems modelling the population densities of interacting species. Recent examples include the influence of habitat degradation and destruction on competing species, or the consequences of including cognitive processes in animal movement models. In this first example, we found how intermediate levels of (negative) impact due to anthropomorphic habitat loss may facilitate coexistence. From an ecological perspective, this can be a very negative outcome when the facilitation is in favour of pests and invasive species. In the second example, the emergence of pattern formation or home range behaviour without the inclusion of a heterogeneous environment is an interesting phenomenon and a relevant contribution to the ecological modelling literature.

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