Need advice about leaving my current PhD and preparing for pure math institutes
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I started a PhD at an IIT (one of the first-generation IITs, but I can't say which one) this June. My PhD is not in the Mathematics department, although my academic background up to my Master's has been in Mathematics.
For various personal reasons that I can't really discuss here, I'm considering leaving the PhD in December. Before I make that decision, I'd really like to hear some perspectives from people who have been through something similar.
Over the past few months, I've had the opportunity to interact with some really good mathematics researchers, and that has made me realise that I genuinely want to pursue pure mathematics. Ideally, I'd like to do my PhD at a research-focused institute such as CMI, ISI, HRI, TIFR, or IMSc. I don't particularly want to join a Mathematics department at an IIT.
At the moment, I have a CSIR JRF with AIR 50. I know that this would not be enough to get shortlisted at these institutes right now, as I would need a rank under 20 for the shortlist. Preparing seriously for TIFR/NBHM this December also doesn't seem realistic because I still have academic and research work to finish here. With proper preparation, I think I could attempt them next year.
So, as of now, I see a few options:
Leave in December, take a job (or do something else), and prepare seriously for the next admission cycle.
Join a Mathematics department at an IIT and give up on the plan of trying for the institutes mentioned above.
Join a local/less demanding institute or university using my JRF, so that I don't have to take up a job, and where the academic pressure is relatively low. I could prepare for the entrance exams/admissions while continuing my PhD there.
Can someone suggest some smaller/local institutes or universities where I could join a PhD using my JRF and have relatively manageable academic requirements? I'd really appreciate some suggestions.
I'd especially appreciate advice from people who have gone through a similar situation or have experience with PhD admissions in pure mathematics in India.