<p>You are going to compete with other Singaporeans with international Olympiad medals so you will have quite a tough time getting in.</p>
<p>With regards to your papers in Mathematics and all that, I think you will need a better grounding in your fundamentals of mathematics - your multivariate calculus, differential equations (ordinary, partial), linear algebra+functional analysis and discrete mathematics before really trying to embark on any sort of research. I’ve met some of the most brilliant individuals in my and my junior batch w.r.t. Mathematics (i.e. SMO Open Champion, IMO Silver) and I don’t they are ready to do any sort of serious research in Math either.</p>