Andrés Ortiz-Muñoz, photo by Doug Merriam

Category theory, a recent development in mathematics, provides a framework to link ideas from various mathematical subfields. It has proven useful in revealing unexpected similarities between apparently different concepts and has suggested ways to merge concepts from two different domains to apply to a third. Researchers have applied it, with profound impacts, to the study of linguistics, programming language theory, and theoretical physics. 

One area with few existing applications of category theory are the life sciences, but incoming Omidyar Fellow Andrés Ortiz-Muñoz, who holds a BS in mathematics and physics from the University of Texas at El Paso and is completing a PhD in biology at CalTech, sees ample opportunities to venture into this unexplored space. 

Chemical reaction networks — theoretical, applied mathematical models that describe chemical systems — are convenient, but
minimal, tools for understanding how systems of interacting molecules behave. One limitation of CRNs is that they are agnostic to the molecules’ internal structure. Category theory could help researchers build a more robust theory of chemical reaction networks that
is more faithful to the structural richness of biological molecules.

Ortiz-Muñoz, who participated in the 2018 Complex Systems Summer School at SFI, plans to draw on existing projects at SFI to inform his research. Research into the thermodynamics of computation, particularly of biological systems; the concept of emergence; and how a better understanding of molecular computation could inform our understanding of the origins of life are all ideas he hopes to explore during his fellowship.