Sales and Trading SA to Quantitative Analyst Full-Time

I know this makes me sound too cheesy and corny to survive on Wallstreet, but my two main passions in life are financial markets and mathematics. I am currently at top tier university double majoring in Mathematics with a specialization in economics, and economics at a school where the economics itself is 70% math and is considered a STEM. I've been trying to secure a summer analyst position super hard last year, and by exhausting all the connections I could with my alumni network, I managed to secure a rotational SA program at Citi for S&T in NY, where I'll be rotating across different products and both sales and trading.

What I really want is to doing a lot of quantitative analysis in my work. So right now, the way I'm going about it is keeping my fingers crossed and hoping I get put on a desk where I would have to analyze quantitative products. From there, if all goes well (which isn't a definite right now), maybe I'll be able to rotate across those desks or other quantitative desks full-time, and maybe end up as an associate on a desk with a quantitative product. I'm also sure that my role will also be more quantitative as a trader rather than in sales.

Could anyone perhaps tell me which products would be the most quantitative if I get any input on which products I have to deal with in my rotation?

Also, even though I get to experience a lot of the different businesses in Citi Markets, I think it doesn't include Quantitative Analysis. Is there any chance I can be a SA in a rotational program and join FT as a quantitative analyst. I know people who did internships as quants would be better suited, but I'd be willing to start a little behind if that's what it took - does anybody know anything about how hard it is to do that, the challenges involved, or if anyone did that?