Let me start by acknowledging the existence of this thread: [Mathematics and cancer research](https://mathoverflow.net/q/87575)


It is well-known that mathematical modeling and computational biology are effective tools in cancer research. When I started college and declared the math major, this was the direction I envisioned myself pursuing. However, I quickly fell in love with algebra, number theory, and "pure" math.


**Are there any ways for an algebraist to contribute to cancer research?**


I've recently learned that algebraic geometry has been useful in studying phylogenetic trees in evolutionary biology, so while I cannot even imagine what an affirmative answer to my question might look like, I am hopeful that one exists.



Algebra and cancer research
You might like to look at this paper:


* Monica Nicolau, Arnold J. Levine, and Gunnar Carlsson, [Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival](https://doi.org/10.1073/pnas.1102826108), Proceedings of the National Academy of Sciences, February 2011.


There is also a lot of other stuff by the same group at
<http://comptop.stanford.edu>


Only a small proportion involves biology, but that might be enough for you.


You might also like to look at the work of Maria-Grazia Ascenzi:


<http://ortho.ucla.edu/body.cfm?id=218&ref=39>


Her PhD is in mathematics but her current work is in biomedical science. I have heard that she is interested in applying algebraic geometry but I do not know the details.


