My area was algebraic combinatorics, which is all about this kind of thing. Combinatorics, representation theory, and geometry share a bunch of objects related

My area was algebraic combinatorics, which is all about this kind of thing. Combinatorics, representation theory, and geometry share a bunch of objects related by some translations from one field to another. So you make progress in one field until you get stuck, then translate to another to make further progress... And repeat.