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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?

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    $\begingroup$ Mathematicians have suggested to use knot theory to model complex biomolecules such as DNA. Another example is Gromov's study of "Mathematical Structures arising from Genetics and Molecular Biology". Reception of these works by biologists is another matter... Link 1 Link 2 $\endgroup$ – Did Sep 14 '16 at 8:57
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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.

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    $\begingroup$ Actually the introduction states explicitely that "the theorems (the book explains) have not made their way into the world of science, but they are directly applicable there" and, despite this last statement, the book does not seem to provide concrete examples of such direct applications. More a program for future developments that the author suggests could happen than actual ones, thus. $\endgroup$ – Did Sep 14 '16 at 8:50
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    $\begingroup$ @Did, yes Spivak's work is very preliminary. Personally, I think that line of ideas will end up having more applications in engineering than science. Only time will tell. $\endgroup$ – goblin Sep 15 '16 at 5:17

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