Hello. I don't typically post on online forums so I apologize if I don't format properly. I'm currently doing an applied math PhD at a state university in the US. I have a bachelors and masters in pure math, and after a brutal application cycle I got in to this particular applied math program very recently. I was originally excited to work on something more marketable, but after about a semester of classes/meeting people I've found that the spark I had during my other work has dwindled, and I find myself wanting to return to pure math.
However, I have no idea even the feasibility of switching programs. I would stay at my current school regardless, but I would like any advice on whether this is possible intra-department, funding, and/or similar experiences. Funding is the biggest limiter for me -- the current professor who I'm TAing for is heavy on the applied side, and I'm uncertain, at best, if there's funding in my school for another pure math PhD. relatively speaking I'm a good pure math student, and can probably get recommendations from people in the department for this change.
As for specifics on research, I'd go either into commutative algebra (most interested in Riesz Algebras) or functional analysis. I'm currently working on applied differential geometry in the form of PDE solving on manifolds.
Thank you for any and all comments.
