EDIT: I take it back, you can buy it now!: https://www.amazon.com/Invitation-Applied-Category-Theory-Co...
In pure mathematics - I found most interesting topics around algebraic topology. Next year, I plan to look into homology. These fields also have computational aspect and some applicability outside of pure maths: computational homology and Topological Data Analysis.
This autumn, I finally looked a bit into category theory (applied) using this good book: https://www.amazon.com/Invitation-Applied-Category-Theory-Co..., and, unsurprisingly, found it exciting.
Regarding PhD in an applied area: I tend to agree with you, and also keep thinking about focusing more on computational / applied mathematics so that my studies could be somehow related to my work. My tech focus at work is around data processing: with interest in distributed databases and computations.
Heh, I see that distributed systems, algebra, topology, and categories are similar in mental representation in my head, they cause same kind of excitement when I study them: visualising, analysing, and playing with the systems of structures, connections, defined rules and operations :)