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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.

trisct
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    This has been often asked. For some interesting informations see for example this post, or this one, or this one etc. You can search for applications of differential geometry to other applied areas yourself. – Dietrich Burde Jan 12 '20 at 09:19
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    Optimization on Riemannian manifolds is an active area of research. But I would say, if you are going to switch to applied math, don't restrict yourself to doing something related to differential geometry, because that is a severe restriction. Just start fresh and go in a direction that is most promising, like computational genomics or something like that. The mathematical maturity you gained by studying differential geometry will help you learn applied math easily. – littleO Jan 12 '20 at 09:42

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