I am currently a third year student in university. So far, most courses I have taken are centered at pure math, with a special focus on differential geometry. However I do start to feel that the pursuit of pure math is a lot harder than I had imagined. So, I am considering changing my focus to something in applied math, without having to starting all over. Also, I should probably start to do some research by now. Is there any field in applied math, where I can make use of all the differential geometry I have learned, so that I don't have to start from scratch?
I'd also like to know whether there is a tight connection between differential geometry and optimal transport theory, or between differential geometry and computational geometry.