What math would I need? (physics-math double major interested in THEP)

[Ege Artan]

So, I am going into my second year in my physics-math double major. For our program, not much specialized math is specifically needed. I love theoretical high energy physics, have been attending seminars in institutes, and been trying to do some reading on my own (it is hard without the math tbh, one constantly feels the need to look up some mathematical idea/object/etc.). I absolutely love complex analysis and differential geometry, I've a couple of textbooks and it is absolutely thrilling to learn something new in these fields. This goes for abstract algebra and representation theory as well. I wouldn't say the same for real analysis but still love it, just not as enthusiastic, and I despise statistics (I know it is important, I probably need to read more to get into interesting stuff).

My question is, for someone who wants to pursue theoretical high energy in the future, which topics would be "needed"? I know one has to be solid in diff. geom. and real analysis, but what else would be beneficial in THEP? I know it is basically impossible for someone to say "you need this this and this", but at least, to be able to keep up with the current research, what would I need solid foundation in? As I've said, I absolutely love these fields but I simply cannot study them all. My course selection is kind of limiting me and I am afraid I may not even be able to take proper upper year statistics courses. I wish I could take them all, love learning, but it is simply impossible and I am at an impasse.

Would it be a good idea to try to cram them all into my upper years so that I can learn them all, or can I leave some (ie stats) of them for the grad school? I really cannot decide on what to prioritize, to take courses that are interesting and may not be as useful, or take courses that are useful but may not be as interesting. What do you think?

Lastly, is it true that we may need some new perspectives in thep? Without a significant breakthrough in plausible experimental predictions, seems like thep has been stagnating for quite some time. Would learning not widely used mathematics fields be logical to maybe have a different perspective? I mean isn't it the case that representation theory really picked up the pace after 1896, and then it made its debut into thep in 1930s? Wouldn't it mean that to accomplish desired progress in thep, one has to be up to date in modern math? Is it different for the current thep, or does a thep physicist has to be an "amateur mathematician" at the same time as well?

Ty for the answer in advance

 

[WWGD]

Isn't it HEPTH; High Energy Physics, Theory? At any rate, re your idea of cramming courses, remember you need to keep a high GPA to be accepted into a reasonable program. I'd suggest taking an amount /type of class that will allow you to keep your GPA at 3.6+.

 

[Vanadium 50]

You got a lot of advice the last time you posted along these lines.

We've been through "I'm too smart for Toronto" and "I'm too smart for my curriculum." This is again a statement that you are being held back - so did you get a 4.0? If not, you should fix that first.

Is it possible that theoretical physics would make more progress if you were to show them the way with better math? Sure. But honestly, I would wait until you had a few accomplishments under your belt before going down this path.

Finally, you might want to ask yourself what a LOR from PF would say if we were to write one. Would it say "He has a very high opinion of himself, but seldom helps others. It's all what we can do for him." And would such a letter help? And will your Toronto letters look any different?