Wilmer Leal » People

Wilmer Leal is a mathematician, chemist, and computer scientist whose research lies at the intersection of applied category theory, computational sheaf theory, dynamical systems, and control. He received his Ph.D. in Computer Science (summa cum laude) in 2022 from Leipzig University and the Max Planck Institute for Mathematics in the Sciences, and holds B.Sc. degrees in Mathematics and Chemistry from the University of Pamplona. From 2023 to 2025, he was a Postdoctoral Associate at the University of Florida with joint appointments in Computer & Information Science & Engineering and Mechanical & Aerospace Engineering. His research develops categorical and sheaf-theoretic methods for compositional reasoning in networked and time-varying systems, with applications to dynamical systems, distributed computation, and nonlinear control. His work has appeared in journals including PNAS, Proceedings of the Royal Society A, and PLOS Complex Systems. Since January 2026, Dr. Leal has been a Research Scientist in the Nonlinear Controls and Robotics (NCR) Group within the Department of Mechanical & Aerospace Engineering at the University of Florida. His current research focuses on integrating category theory and computational sheaf methods with Lyapunov-based and learning-enabled control of complex nonlinear systems.

Research Interests

Applied Category Theory
Computational Sheaf Theory
Nonlinear Dynamical Systems
Networked and Distributed Systems
Compositional Modeling and Reasoning
Learning-Enabled and Lyapunov-Based Control
Topological and Geometric Methods for Data Analysis

Teaching Interests

Applied Category Theory for Engineering
Dynamical Systems and Control
Network Science and Complex Systems
Computational Sheaf Theory
Data Science and Scientific Computing

Publications

Leal, W., Bumpus, B. M., Nickel, J. K., García, J., Fairbanks, J., & Dixon, W. E. (2026). Time-Varying Data as Sheaves: An Invitation to Narratives. Submitted.

Bumpus, B. M., Leal, W., Karvonen, M., Simard, F., & Fairbanks, J. (2026). Towards a Unified Theory of Time-Varying Data. Applied Categorical Structures.

Leal, W., Llanos, E., Bernal, A., Jost, J., Stadler, P. F., & Restrepo, G. (2022). The expansion of chemical space in 1826 and in the 1840s prompted the convergence to the periodic system. Proceedings of the National Academy of Sciences (PNAS).

Teich, M., Leal, W., & Jost, J. (2025). Diachronic data analysis supports and refines conceptual metaphor theory. PLOS Complex Systems.

Di Lavore, E., Leal, W., & de Paiva, V. (2025). Dialectica Petri Nets. Fundamenta Informaticae.

Llanos, E., Leal, W., Bernal, A., Jost, J., & Stadler, P. F. (2024). Are the chemical families still there? The formal structure of similarity of elements and its thermochemical domain. Proceedings of the Royal Society A.

Llanos, E., Leal, W., Luu, D. H., Jost, J., Stadler, P. F., & Restrepo, G. (2019). Exploration of the chemical space and its three historical regimes. Proceedings of the National Academy of Sciences (PNAS).

Notable Awards

DAAD Doctoral Fellowship, German Academic Exchange Service (2017–2022)
Graduated summa cum laude, Leipzig University (2022)
Selected Participant, 71st Lindau Nobel Laureate Meeting (2022)
Selected Participant, American Mathematical Society Mathematics Research Communities (2022)
Selected Participant, Applied Category Theory Adjoint School, MIT (2020)