What are the topics in theoretical and mathematical physics?

[Eslam100]

I'm a rising physics sophomore at a Japanese university. I've studied general physics, linear algebra, and analysis (actually, calculus of single and several variables with emphasis on analysis, everything was proven and the theoretical background was well explained)
Other than that, I've self-studied the very basics of distributions, Hilbert spaces, Lebesgue integration, local form of Maxwell’s equations, and calculus of variations. not rigorous though I'm interested in fields, high energy physics(specially, particle and astroparticle physics) and mathematical analysis.

I'd like to work on something that is suitable for my level. I'm also fine with self-studying other subjects to reduce the gap to a certain interesting research topic.

Can someone help me with that?

 

[jedishrfu]

Can you give us an idea of your interests?

Where do you hope to be in 5 or 10 years?

Do you plan to practice as a mathematician or as an experimental or theoretical physicist?

 

[Eslam100]

I plan to be a theoretical physicist. I'm interested in both theory and how the mathematics is used to describe the nature of the universe. I'm fascinated by the idea of symmetry and how a lot of physical phenomena can be described in terms of symmetry. I'm also interested in symmetry breaking. However, I don't have enough math and physics to understand such concepts so I'm welling to self-study a lot and accelerate my learning curve to get faster to research.
It would be great if i can do some kind of high quality research at a young age.
So as you can see, I'm into academia. I hope I can understand the world better and add something valuable to it along the way.