I am a second year physics undergrad. After spending about an year exploring mathematical physics (QFT,solitons, etc), I have realized that maybe theoretical physics isnt my passion after all, and I am thinking of changing my emphasis to maths, so that I would be able to pursue research after my undergrad in math. I would like to know, how should I go about studying maths so as to complete the maths undergrad syllabus which would enable me to apply for grad school after 3 more years, and also pursue a specialized research area simultaneously. Currently, I don't have anything on mind specifically. I have studied a bit of topology, and group theory both from mathematical physics textbooks. I am thinking of something on the lines of algebraic number theory, or algebraic geometry. What are the prerequisites for studying each of these? What should I study so that I would be able to study these by this summer? Also, what is the maths that I should know other than that requires for these areas. Please bear in mind, I come from a college, where shifting to a formal maths course is now impossible, and I have very little choice to chose my courses. Most of them are compulsory physics courses.
I have heard algebraic number theory and algebraic geometry require lots of prerequisites, which I may not have the time to do. Could someone recommend similar fields where I am in a position to do research with less pre-study.