Me in a nutshell

I started my undergraduate studies at Universidad Nacional Autónoma de México (UNAM), where I pursued a bachelor’s degree in Pure Mathematics under the guidance of Dr. Hugo Rincón. During this time, I developed a strong interest in algebra and its formalism, ultimately writing my bachelor’s thesis summarizing key results in rings, fields, and Galois Theory. Subsequently, I enrolled in a master’s program at UNAM, where I delved deeper into the study of algebraic structures. This time, my master’s thesis focused on Abelian groups that are not the additive structure of a ring. Following this, I pursued my PhD at UNAM, where I conducted research in Category Theory, Lattice Theory, and Module Theory. Specifically, I explored properties relating the category of modules, and a particular category of lattices which has modular lattices as objects and “linear lattice morphisms” as morphisms. This approach became my first line of research, in which I replicate or “categorize” module-related properties into their lattice counterparts.

After completing my PhD at UNAM, I undertook a postdoctoral appointment at the University of California, San Diego (UCSD), under the direction of Dr. Gabriel Silva. During this time, we engaged in research involving a mathematical framework that formalizes biological neural networks using Category Theory. This line of research encouraged us to use categorical notion and structures for studying neural network dynamics and its emergent behaviors; a topic that has the spotlights due to their connections to Machine Learning and Large Language Models. Within this line, we believe that its applications could pave the way for a new avenue of research elucidating and characterizing the brain’s high complexity. Consequently, this could furnish mathematical frameworks associated with a new era of AI.

Preprints and Publications

  • 2025 Pardo-Guerra S., Vivek G., Silva G., “On The Graph Isomorphism Completeness of Directed and Multi-directed Graphs”, Mathematics 2025, 13, 228. (Feature paper).
  • 2025 Jingze Li J., Pardo-Guerra S., Basu K., Silva G., “A Categorical Framework for Quantifying Emergent Effects in Network Topology”, Neural Computations.
  • 2024 González-Bayona F., Pardo-Guerra S., Rincón-Mejía H., Zorrilla-Noriega M., “On semi-projective lattices”, submitted at International Electronic Journal of Algebra.
  • 2024 Pardo-Guerra S., Silva G., “On preradicals, entropy, and persistence”, International Journal of General Systems, 1–25. https://doi.org/10.1080/03081079.2024.2348665.
  • 2024 Pardo-Guerra S., Vivek G, Roldan J., Morar V., Silva G., “Extending undirected graph techniques for directed graphs via Category Theory”, Mathematics 2024, 12, 1357. https://doi.org/10.3390/math12091357. (Feature Paper, Editor’s choice)
  • 2023 González-Bayona F., Pardo-Guerra S., Rincón-Mejía H., Zorrilla-Noriega M., “On torsion theories and open classes of linear modular lattices”; Communications in Algebra, 0 (0) , 1-21.
  • 2023 Pardo-Guerra S., Rincón-Mejía H., Zorrilla-Noriega M., González-Bayona F., “On the lattice of conatural classes of linear modular lattices”, accepted at Algebra Universalis.
  • 2021 Pardo-Guerra S., Rincón-Mejía H., Zorrilla-Noriega M., “Big lattices of hereditary and natural classes of linear modular lattices”, Algebra Universalis, 82(4), 1-15.
  • 2018 Pardo-Guerra S., Rincón-Mejía H., Zorrilla-Noriega M., “Some isomorphic big lattices and some properties of lattice preradicals” Journal of Algebra and its Applications, 19(07), 2050140
  • 2016 Jaramillo N., Pardo-Guerra S., Ramirez-Galarza A., “Manual of strategies to solve Analytic Geometry exercises”, Publications of Faculty of Pure Science, National Autonomous Mexican University (UNAM).

CV

Here you can find my complete CV

Prime graph’s code

Here is the code we use in our paper relating directed graphs and prime graphs: https://github.com/vgeorgeucsd/prime_graphs.git