I recently graduated with an undergrad mathematics degree, and I am really interested in pursuing mathematics research. My main interests lie in the geometry and topology of spacetime/ the universe in general, so some areas of mathematical physics. My interest really comes from space-time paradoxes. I was wondering what areas of mathematics I might read to learn more about this field.
My knowledge in geometry and topology is at the level of someone that has taken an honors course in differential geometry, algebraic topology and low-dimensional topology. I have also studied honors level general relativity.
From what I read online, a good area to focus on is mirror symmetry (string theory) and hyperbolic geometry. Should I be looking for other research areas?
I apologise in advance if this question is not meant for this platform, I will take it down if that is the case, please let me know where I might be able to ask the question.