math research for Caltech

<p>I'm planning to apply at Caltech and I have made a math research related to the applications of modular arithmetics in invariants. Do you think that is a good topic ? If no what other topics would you suggest me for math ( my strongest areas are Combinatorics and Number Theory )
What about the combinations math-biology or math-physics. Are these kinds of researches better than pure mathematics ones ? Which ones do colleges prefer ?
Thanks in advance for your answers</p>

<p>caltech is not very picky about what kind of research you do, as long as it is good. if you have made some real mathematical progress, try finding a local faculty member at a university to read it and give advice. consider eventually submitting it to a journal.</p>

<p>How advanced does it have to be in order to be considered good?</p>