Not meaning to derail an interesting conversation, but I'm curious about your description of your work as "applied probability". Can you say any more about what that involves?
Pure probability focuses on developing fundamental tools to work with random elements. It's applied in the sense that it usually draws upon techniques found in other traditionally pure mathematical areas, but is less applied than "applied probability", which is the development and analysis of probabilistic models, typically for real-world phenomena. It's a bit like statistics, but with more focus on the consequences of modelling assumptions rather than relying on data (although allowing for data fitting is becoming important, so I'm not sure how useful this distinction is anymore).
At the moment, using probabilistic techniques to investigate the operation of stochastic optimisers and other random elements in the training and deployment of neural networks is pretty popular, and that gets funding. But business as usual is typically looking at ecological models involving the interaction of many species, epidemiological models investigating the spread of disease, social network models, climate models, telecommunication and financial models, etc. Branching processes, Markov models, stochastic differential equations, point processes, random matrices, random graph networks; these are all the common objects used. Actually figuring out their behaviour can require all kinds of assorted techniques though, you get to pull from just about anything in mathematics to "get the job done".
In my work in academia (which I’m considering leaving), I’m very familiar with the common mathematical objects you mentioned. Where could I look for a job similar to yours? It sounds very interesting
Sorry, I'm in academia too, but my ex-colleagues who left found themselves doing nearly identical work doing MFT research at hedge funds, climate modelling at our federal weather bureau, and SciML in big tech. I know of someone doing this kind of work in telecoms too, but I haven't spoken to them lately. Having said that, it's rough out there right now. A couple of people I know looking for another job right now (academia or otherwise) with this kind of training are not having much luck...
