Our research focuses on the study of the formation of patterns in complex systems such as the growth and form of living matter, and the emergence of collective behaviour in active systems. Also, we use data-driven methods to learn the underlying physical laws of these complex systems.
Our approach is eclectic and driven by curiosity. In the group, we use Theory, Experiment, and Simulation, to Test ideas (We are a TEST Lab :-). We thrive to gain insights into diverse problems at the interfaces of applied math, science, and society. Current research topics of research are described below.
Active Soft Matter
The questions we study here concern the study of slender structures such as filaments. Indeed, whether active or passive, matter that has the form of filaments can be observed at all scales in nature. Examples include DNA, filoviruses, elongated bacteria, fungi, neurons, arteries, hairs, snakes, eels, beams, cables, plants stems, trees, elephant trunks, solar flares, and galactic filaments. Although these elongated structures are three dimensional, it is possible to exploit their slenderness to deduce dimensionally-reduced models. Many studies have been performed when the constituent matter of these structures is made of passive substance, as is the case of beams, cables, strings, etc. However, for living filamentary structures, like plants stems or neurons, there are still deficiencies in our understanding due to the lack of a general constitutive theory relating the growth to the stresses. Here the challenge is that the process in which the local mechanical, biochemical and genetics couple to provide a constitutive law of growth is an open problem. Important recent progress has been made in exploring the effect of mechanical forces on morphogenesis. Our goal here is to develop a paradigm for establishing a general growth principle for these living structures.
Pattern Formation
In many of the problems we consider, active elements or agents interact at local level to produce a hierarchy of complex patterns, or some collective behaviour. The main challenge of these problems is that they are multi-physics, multi-scale, and multi-phase. Yet, they can be all cast in terms of complex systems. We mean by complex system, a system with a high degree of liberty. Once the problems are cast mathematically in term of differential equations, we study their (in)stability to perturbation.
Machine Learning
We combine data-driven, computational, and theoretical approaches to learn the underlying laws amongst interacting active systems. In particular, we use statistical optimisation and sparsity promoting techniques to perform scientific machine relevant to active matter.
Societal Mathematics
In the group, we also apply the tools of complex systems and active matter to solve societal problems. This application of our research comes from the fact that when growing up in West Africa, I experienced situations in which the use of mathematical modelling could have had a big impact in improving the lives of many people. As an applied mathematician who saw the disruptive impact of COVID-19, Malaria, and locust infestations, I am interested in using mathematical modelling as a way to give back to society by applying the techniques and tools of complex systems to address scientific questions that arise in society in general and developing countries in particular. I coined the term "societal mathematics" as the use of math for social good.