I'm from the top math university in my country (it's not really world class but on average one guy from every other batch in my uni goes to Harvard/MIT/Princeton/UChicago/Stanford/UMichigan for PhD).
I'm in my second year and I'm broadly interested in number theory and geometric analysis, but there's no "good" faculty in number theory in my university (there's only one prof and he don't do any active research and don't have much reputation outside my country), so I'm almost on my own to study number theory.
It's pretty hard to learn everything by myself with simultaneously handling the coursework, so I'm wondering whether it's a good/sensible idea (wrt say grad school application where I need to compete with many people from top colleges in USA who are taking legit number theory courses by world class number theorists) to switch completely to geometric analysis and ditch number theory ? I think I can focus more on geometric analysis in that way too -- the only thing that is bugging me from switching completely is that I like number theory more than geometric analysis.
There were one guy from my college who went to Princeton for number theory who wrote a solo number theory paper as an undergraduate, but I'm nowhere close to being that smart. Also I can do reading courses/summer internship under some active number theorist researchers in my country, but the problem is that you need to know some nontrivial amount of number theory before you can do some internship under some reknowned number theorist !