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!

Brickwall

It's really unfortunate when suddenly you get ... stopped.  Writer's block kinda?  I tried to redirect toward some of the more visual parts of my thesis, making images, and so on.. but then I got blocked again. So, I'm putting my thesis aside for two or three days, working out like crazy, preparing for my Analysis exam, and watching some South Park and Doctor Who.  It feels pretty nice.

Meanwhile, I hear the rapture is happening in a little less than a month...

No more...

These Lyapunov coefficients are really crazy, let me tell you.

Chugging away at the thesis, teaching at the end of the semester, making graduate school decisions, making moving decisions, planning a wedding... oyvey.

Theorem proved!

Bogdanov-Takens bifurcation theorem proved and dust-bitten.  Taking a step back to the Andronov-Hopf bifurcation theorem in order to move forward to the Bautin (or generalized Hopf, or perhaps Bautin-Hopf would be more appropriate) bifurcation theorem.  I learned from my mistakes with the BT bifurcation, which is to err on the side of the general rather than the specific (although explore specific examples in order to get a general intuition).

Blah. Blah. Blag.

Vaguely embarassing

You know when you get all stubborn and convinced you can do something all by yourself, and then when you get stuck, you get REALLY stuck because you're stubborn and you're convinced that your method is the correct method, and so on? Yeah, and when you keep getting the (same) wrong answer in several different ways? Yeah, just go in for help.

Trust me on this.  Some scientists and mathematicians are able to perform research in seclusion.  You, like me, probably aren't one of them. It's okay, nothing to be ashamed about.  Just remember that science as a mechanism for explaining reality is more than the sum of the contributing scientists, and there is a reason that scientists attend conferences, people!

Seriously.  Go get help, it won't hurt, I promise.

P.S. Bifurcation proven!