Complexity Postdoctoral Fellow
Omidyar Postdoctoral Fellow
Andrés grew up in the city of Juarez, Mexico just south of El Paso, Texas. When the economic recession of 2008 began, Juarez, a city infamous for its crime and violence, effectively became a war zone. That state of affairs lasted for about four years. At that time Andrés was an undergraduate at the University of Texas at El Paso (UTEP), studying mathematics and physics. During weekdays he had the privilege of escaping the violence affecting his hometown to spend time thinking and learning about some of his favorite subjects such as abstract algebra, logic, and the foundations of mathematics. It was then that he first learned about category theory, a subject that has fascinated him ever since. A lifelong interest in the brain and the human mind led him to get involved in an undergraduate research program in bioinformatics at the University. He was, however, captivated by the striking similarity between formal mathematics and biology at the molecular level. Both displayed an impressive morphological diversity despite being assembled from a comparatively small number of components and rules. His fascination landed, almost serendipitously, right at home when he began a summer internship at the Novartis Institutes for Biomedical Research in 2011, in collaboration with Harvard professor and former SFI external faculty Walter Fontana. Professor Fontana had been captivated by a similar observation years before as a postdoctoral fellow at SFI, where he developed a formalism for understanding biological organization at the chemical level based on the lambda calculus.
After graduating from UTEP in 2013 Andrés returned to the Fontana lab to work on mathematical aspects of polymerization before starting his Ph.D at Caltech. Walter Fontana and Andrés have continued to collaborate over the years, focusing on the combinatorics of molecular assembly systems. At Caltech Andrés joined the lab of Erik Winfree, who is one of the pioneers in the field of molecular computing, to work on the mathematical theory of stochastic chemical reaction networks (SCRNs). Computing probabilities and counting combinatorial structures may appear on the surface to be completely different kinds of problems, but such distinction ceases to be significant upon closer examination, as Andrés found out in his explorations. The first indication of the latter is that both kinds of problems are often elegantly handled by means of generating function techniques. Methods from category theory reveal that all generating functions are inherently combinatorial, an observation that can be used to reveal a wealth of combinatorial structures hidden in probabilistic systems. Chemistry, and even more so biology, is imbued with combinatorics, which makes the probabilistic-combinatorial connection all too practical when it comes to systems that are simultaneously chemical and stochastic, such as the SCRNs that Andrés studied during his Ph.D.
Andrés’ time in the Winfree lab, with its strong emphasis on the computational abilities of molecules, was instrumental in consolidating his vision of mathematical biology, which seeks to establish a formal equivalence between chemistry, mathematics, and computation via stochastic chemical systems. Andrés hopes to pursue this vision as an Omidyar Postdoctoral Fellow at the Santa Fe Institute. In addition to his above mentioned interests, Andrés is also interested in bringing ideas from pure mathematics, in particular higher category theory and homotopy type theory, to the study of complex systems, especially in areas where conventional mathematical techniques have proved to be inadequate.
Andrés received his B.S. in Mathematics and Physics from the University of Texas in 2013 and his Ph.D from the California Institute of Technology.