<p>Math is very much a who you know field. I can see a LAC graduate being viewed with suspicion if she hadn’t any recommendation from a known or respected mathematician. These are at research universities, rarely at LACs. </p>
<p>This argues for a university rather than LAC. The university doesn’t even have to be a top 12, but it does need a very good mathematician in your topic on faculty. Then if you work with said mathematician and stay on the PhD track, s/he can help.</p>
<p>Go to AMS (American Math Society) site and check out who is working in your field. Email their departments - there is a directory of math departments on the site with phone and email info - and see if you can make contact.</p>