TITLE: Algebra and cancer research
QUESTION [27 upvotes]: Let me start by acknowledging the existence of this thread: Mathematics and cancer research
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.

REPLY [3 votes]: Contributions of algebraic methods for cancer research are needed i.a. for data analysis and for modeling.
European Association for Cancer Research (EACR):
2 Postdoctoral Positions, Machine Learning, AI, Abstract Algebra, Champalimaud Foundation, Lisbon, Portugal, 2020
"The aim of the positions is to develop theory and methods related to an approach to AI based on Model Theory and Abstract Algebra, read here": Martin-Maroto, F.; De Polavieja, G. G.: Algebraic Machine Learning. 2018
Methods for modeling of biochemical networks and bionetworks (i. a. for cancer) are e.g. neural networks, Petri nets, systems of differential equations, systems of integro-differential equations and the algebraic methods used for that.
Sassone, V.: The Algebraic Structure of Petri Nets. 2000

F. Brouwer, A. F.; Meza, R.; Eisenberg, M. C.: A systematic approach to determining the identifiability of multistage carcinogenesis models. Risk Anal. 37 (2017) (7) 1375–1387
Closed-form solutions could be one means to help deducing new knowledge about unknown interrelations. Closed-form solutions for the above-mentioned methods would be nice.