This was originally a question posted here on MathSE. But I'll ask again here to see if I can get some different answers.
I'm looking for current areas of research which apply techniques from differential geometry to biological processes. I'm (scantly) aware of a handful of applications to cell science and microbiology, but I've heard almost nothing of differential geometric methods in say ecology or evolution. Any sort of reference (textbook, paper, researcher, etc) would be appreciated.