Hi Benjamin,

I am delighted that you are passionate about mathematics. That is a great start!

Now, there are many areas of research in applied mathematics. From my research program, I work on various projects emerging from cellular and developmental biology where mathematics plays a pivotal role in understanding mechanisms for single and collective cell migration and the formation of pattern formation in nature. Typical projects involve data-driven mathematical modelling involving both continuum mechanics and semi-linear parabolic partial differential equations (of which ordinary differential equations are a subset of); rigorous mathematical analysis of such problems (e.g. existence, uniqueness of solutions, linear or weakly nonlinear analysis in the context of asymptotic analysis); development of novel numerical methods to solve the models both in space and time (in some cases, when the space itself is part of the solution being sought), their rigorous numerical analysis (existence, uniqueness, positivity, boundedness of strong or weak solutions depending on the numerical method developed), applications of the models to experimental observations and finally, to close the loop, using data to constrain the models through model selection and parameter inference (here one needs to develop optimal control or Bayesian methods to fit models to data and to carry out parameter estimation). Within this cyclic research approach, one can find many projects to study, either from a theoretical, analytical, numerical, computational and statistical point of view. The choice really depends on one’s mathematical strengths and expertise as well as the passion to learn new methodologies and techniques. Applications of such models are prevalent in cancer biology, wound healing, burns, inflammation, and many others.

Other areas of research in applied mathematics include epidemiology, infectious diseases, material and biomedical sciences, population dynamics, game theory, economics, climate modelling, fluid dynamics, etc.

I am super happy to chat to you more specifically about applied mathematics in my research area. I hope you find this reply useful, if not, get in touch, happy to provide further clarity to the reply.