Queueing theory turns out to be a big part of the system I'm working on, as do graph traversals. I'm not proving anything new, but I am certainly transforming known solutions to be present implicitly in the way data flows through the device (a network gateway).
I've also done work on numerical solutions, implementing various formulae the researchers have come up with, and dealing with various optimization (in the mathematical sense) problems.
Lately there has been a lot of talk on "new classic" things, applying machine learning algorithms to data sets, and finding relevant classifiers and adjustments to the ML algorithms that provide better results. Hopefully I'll get into implementing and doing real work on that soon.
I do work in academia though, in a department focused on implementing research in ways that industry can actually use it.