It seems I'm about to have a bad application season, as all schools I'm waiting to hear from have given out offers of admissions to other applicants. I'm trying to come up with a viable plan to turn my application into a successful one for next year's season.
Here are some important things to note:
I come from an unknown school, but my reference writers earned their Ph.Ds from well-known schools in the U.S. (top 25 via NRC ranking). They all encouraged me to apply to top 30 programs in the US.
I am an international applicant.
I am interested in pure mathematics.
Some fall-back plans I have is to actually get involved in research during the summer and fall, and I'm hoping I can get a serious publication out of doing this.
So for the people who have served on admissions committees in the past, what else can I do? Should I not bother to apply to the same programs I applied to this year?