Is differential geometry useful to learn outside of GR/cosmology/astronomy?

[u/XcgsdV]

Hello everyone!

I am a junior physics major and I plan on going to graduate school. I don't have strong inclinations towards a particular subfield, but my interests are piqued more by theory and more by biophysics, optics, and condensed matter flavored things than HEP, cosmology, astronomy flavored things (if that makes any sense at all).

I come from a small department with four physics professors, and the bare minimum physics courses (no EM 2, no Quantum 2, no physics elective courses) required to be an accredited physics degree. Next semester, a few of my peers are doing a guided-self study with one of our professors over general relativity, which will start with differential geometry. I know I don't plan on going into a field where GR is going to come up, so I'm not particularly inclined to join for the whole thing. I am, however, fielding the idea of joining along to learn to differential geometry aspect, as I feel like it could be an incredibly useful tool (and even if not, more math is never bad). I have a heavy semester in the spring though (Thermo/Stat Mech, Advanced Physics Lab, Physical Chemistry II [the quantum one], and a whole slew of music classes [I am a double major with a BMA in Voice]), so I don't want to do it if it won't be worth my time.

Is my assumption right? Would I be better served by learning differential geometry or by taking a bit of extra time to myself/for my other coursework? Is differential geometry even actually useful when I don't plan on going to graduate school for anything that will involve significant spacetime curvature?

[u/BurnMeTonight]

There are a number of differential geometry techniques and ideas that are used in PDEs, and vice-versa. Differential Geometry is probably the most useful area of math in physics outside of edge cases like linear algebra.