I am a math major and I am trying to figure out an area to go into for my PhD. I want to apply my math into biology, specifically proteomics or biological membranes, but I am not very familiar with the field of Bio Math, are there any problems in biology that require deeper and more abstract math (group theory, geometry, topology, etc)? Are there any review papers or literature that I could look at to help me figure out my PhD?
You might find David Spivak's ideas relevant. He (tries to) apply category theory and related frameworks to sciences where deep math is typically absent.