I've been exposed to geometric algebra a few times, but for me to be motivated to dig into it I would need to see a few examples of how it can drastically simplify certain calculations. Otherwise there's just so much math out there to learn with more common direct applications that it's hard to justify the effort.

For example, is there a way to use geometric algebra to better handle tensor manipulation (decomposition etc.)? That all gets pretty messy once you leave matrices and vectors.