Former Math Prof, turned Econometrician / Statistician / Machine-Learning type (anything empirical), particularly in finance (i.e., P-measure most certainly, not Q-measure except when I have to).
My interest is in all things statistical, ill-posed, over-determined or under-determined, the linear algebra and tensors I need to get things done, the probability needed (CLT, LLN, Large deviations, and other asymptotics). I also enjoy the philosophy of probability.
I would be a Bayesian, but it takes too much effort.
My PhD was on Calculus of Variations, and I did work in nonlinear Elliptic PDE, some Harmonic Analysis, and touched on both elasticity and image processing. The image processing work (Mumford-shah functional) is very closely related to regularisation methods in machine learning, useful for trend-following and systematic trading.