Mauricio Montes
Short Bio
PhD student in mathematics at Auburn University and currently a visiting researcher at Sorbonne University. My work lies at the intersection of applied algebraic topology, category theory, probabilistic models, and chemical reaction networks. I am especially interested in using topological and categorical structure to understand when complex dynamical or inferential systems can be reduced without losing the quantities of interest.
Education
Bachelor of Science The University of Texas at Austin 2021
Doctor of Philosophy in Mathematics Auburn University Expected 2027
Professional Experience
Visiting Researcher, Sorbonne Université, Paris, France, 2025–2026.
Conducting research on probabilistic graphical models, belief propagation and chemical reaction networks under the supervision of Grégoire Sergeant-Perthuis.
Summer Associate, Institute for Defense Analyses, Washington, DC, 2025.
Worked on statistical modeling, uncertainty quantification and data analysis for defense sustainment applications.
Research Fellow, Los Alamos National Laboratory, Los Alamos, New Mexico, 2026.
Will conduct research with the Center for Nonlinear Studies on information-preserving graphlet compression for uncertainty-aware machine learning.
Innovation
My research lies at the intersection of applied algebraic topology, category theory, probabilistic inference and chemical reaction networks. I use structural mathematical tools to simplify complex networked systems while preserving information relevant to their dynamics, steady states or inferential behavior.
Recent work includes a categorical approach to chemical reaction network reduction, where topological reductions are interpreted through stoichiometric functors and Schur-complement constructions. I also study chemical reaction networks that implement belief propagation, with the goal of transporting reductions of probabilistic graphical models to their associated reaction networks while preserving the inferred quantities of interest.
More broadly, my research connects applied topology, sheaf theory, graphical models and scientific computation, with applications to biochemical networks, probabilistic inference and machine learning.
Engagement
I founded the Directed Reading Program at Auburn University, which pairs undergraduate students with graduate student mentors for semester-long independent reading projects in mathematics. Through this program, I have mentored students on topics including algebraic geometry, homological algebra, Fourier analysis and abstract algebra.
I also co-founded the Topological Data Analysis Reading Group at Auburn University, where I helped organize and lead lectures on applied algebraic topology, persistent homology and related topics for students and researchers interested in topology and data analysis.
Publications
Categorical Perspectives on Chemical Reaction Networks, with Justin Curry. arXiv:2604.04919.
Reduction of Probabilistic Chemical Reaction Networks, with Grégoire Sergeant-Perthuis. Accepted at ICML 2026.
Talks and Posters
“What is the Shape of Data?” Auburn Graduate Student Seminar, October 2023.
“Sheaves and Chemical Reaction Networks,” Auburn Graduate Student Seminar, March 2025.
“Categorical Reductions of Chemical Reaction Networks,” London-Oxford-Paris TDA Seminar, London, November 2025.
“A Categorical Perspective on Reductions of Chemical Reaction Networks,” SALTO Workshop, Paris-Saclay, December 2025.
“Perspectivas Categóricas de Reducciones de Reacciones Químicas,” Jornada de Topología de Datos, Sevilla, February 2026.
Awards and Fellowships
Chateaubriand Fellowship, 2025–2026.
GEM Fellowship.
Auburn University Presidential Graduate Research Fellowship.
