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?