I'm closing in on the end of my undergraduate degree, and it's time to start thinking about where I want my career to go. I feel as though I'm headed for algebra. I'm currently reading a Springer text on homological algebra and loving every page. However, I'm often investigating various other mathematical fields with great interest, from graph theory to analysis.

I don't want to base my entire career around pumping out papers, but I suspect it's a good idea to get an early start on producing publications, and hence I'd like to start working on research. (there are some open problems that I love & put effort into, but they're all way beyond me currently) It's also happened all too often in the last several years that I've come up with a seemingly novel idea, or interesting theorem, only to discover it's been done (and sometimes a while ago). I'm desperate for the joy of contributing something new.

Are there any areas of research that seem to be ripe for the picking? Any new fields emerging that are promising?