Neuroscience or algebra?
Blog fiends! My semester of hell is officially over. My round of applications to graduate school were all rejected; I was shooting way too high in terms of quality of school, given my record (although not necessarily my capability). My wedding is coming up in 2 months, but the planning is nearly complete (barring, of course, the last minute rush). I only have one proof left on my thesis (and then figures and prosy exposition). It is a long, tedious proof, and not particularly instructive to the reader, so I'm considering taking the applied-mathematician-out by demonstrating with numerical simulations that my claim is true. Worst-case (best case?) I'll be tossing the proof into the appendix anyhow. I take my preliminary exam in Real and Functional Analysis in 2 weeks here, so that will be nice to get out of the way. I'll be moving next month... and I'm done teaching the 4-week summer session at the end of next week.
Basically, what I'm saying is that while I still have a lot on my plate, each and every week - in fact, nearly every day - my schedule is loosening up. It feels really good. But this brings me to a problem: what to do next?
Yeah, you probably think I'm crazy; with a move, a wedding, a thesis, and an exam, why in the world would I concern myself with what comes next? Well, in particular, I've basically been shut down from the computational neuroscience community. It sucks hardcore; my advisor in neuroscience left a year after I got into grad school, and I was consequently expected to pick a thesis topic, write it, teach myself the latest neuroscience, and look into PhD programs all on my own.
Let me tell you: don't do that. You're not going to have a good time, and it won't necessarily be good for your career. I would love to get into computational neuroscience and apply some mathematics, but I have no "in." I can try to write a paper or two by myself and get them published in Neuron or the Journal of Computational Neuroscience, but... well, without an advisor, that task seems a bit daunting. The paper I was writing criticizing the Cheadle model has fizzled; my previous advisor entirely lost interest in the project after leaving academia, and at this point, I'm submitting it to the Journal of Vision on a whim... in the end, writing a paper that criticizes a bad model isn't the greatest way to establish yourself as a good modeler.
So, I believe that this fall I will be changing the direction of my research entirely away from applied mathematics and computational neuroscience. I believe I will be going into commutative algebra with Jim Coykendall, investigating power series rings (possibly with a measure theory flavor to it) rather than try to battle my way into a scientific discipline that doesn't really want or need me. This will have a couple of wonderful effects on my career. For one thing, I'll have an advisor. For another thing, I'll have a freaking advisor.
Has anyone out there experienced something similar to what I've experienced? I've been left in the lurch, scientifically speaking, before I was able to develop a network of people with whom I could work and before I was able to develop a body of work and a foundation of knowledge I could rely upon. I've spent the past 3 years getting up to date on spiking neuron models and measures of synchrony in time series to analyze networks of these neurons and then... it appears I have no future in that career.
I could apply to schools again in the fall, but my CV won't have changed. I could get into a summer school program for computational neuroscience for a crash course to network with folks and to expand my knowledge. I could come up with something - anything, a small mathematical result with consequences in simple neural models - and try to present it at conferences. Speaking of which, I could just blow a bunch of money this year traveling to a bunch of conferences and networking. But this would all preclude applying again this next year, which would add a one-year delay for my career.
Or, I can just throw up my hands and go into algebra, immediately start working on a pretty sweet dissertation with a really awesome advisor, and give up the computational neuroscience ghost.
Tell me what to do!