Published
A p-adic reaction-diffusion model of branching coral growth and calcification dynamics
Fuquen-Tibatá, A., Cortés-Poza, Y., & Pérez-Buendía, J. R. (2026). Journal of Mathematical Biology.
☕️Jesús Rogelio Pérez Buendía
Investigador por México · SECIHTI · CIMAT Mérida
Professional Summary
Mathematician, Researcher for Mexico at CIMAT Mérida (National System of Public Research Centers). Affiliated with the Secretariat of Science, Humanities, Technology and Innovation (SECIHTI). I work at the intersection of arithmetic geometry, number theory and dynamical systems, with emphasis on p-adic methods and applications to mathematical biology.
Education
Ph.D. Mathematics — Concordia University
M.Sc. Mathematics — IMATE-UNAM
B.Sc. Mathematics — FC-UNAM
Interests
Geometría aritmética
Geometría algebraica
Teoría de números
Geometría p-ádica (rígida, Berkovich)
Cohomologías p-ádicas y teoría p-ádica de Hodge
Geometría logarítmica
Sistemas dinámicos aritméticos (p-ádicos, no arquimedianos, cuerpos finitos)
Dinámica Aritmética
Dinámica no arquimediana
Matemáticas Condensadas
Dinámica condensada
Álgebra conmutativa
Criptografía y teoría de códigos
Biomatemáticas
FMAT–CIMAT Colloquium
I am a co-organizer of this joint colloquium (since 2017). Schedule, announcements and materials for 2026:
Official site — FMAT–CIMAT Colloquium 2026 (Google Sites, cimat.mx domain)
Research
My work is organized around arithmetic geometry and p-adic methods, linking p-adic Hodge theory, Galois representations, rigid and logarithmic geometry, Berkovich spaces, and related lines in pure mathematics.
The core of my research brings together arithmetic geometry and arithmetic dynamics. On the dynamics side, I study iteration and the structure of maps in non-Archimedean settings (p-adic and related), and also over finite fields, congruence rings, groups, and the algebraic–geometric objects that arise in these contexts. Taken together, these lines have their own intrinsic mathematical motivation. Applications—including systems biomathematics, cryptography, and other connections to applied work—are further uses of selected ideas and techniques; they do not by themselves delimit the scope of the program.
I am a founder of the P-ADAGIO group (P-adic Arithmetic, Dynamics And Galois-Informed Observations), a multi-institutional initiative focused on dynamics over the Fargues-Fontaine curve, Berkovich spaces and Clausen-Scholze condensed structures.
Software development
Self-contained tools (HTML/JavaScript) linked to research and outreach, with no application backend on this server.
- p-adic GRN Suite — p-adic analysis of Boolean gene regulatory networks: p-adic balls (E/A/I), optimal ordering, ANF and interactive visualization. Registered software (Zenodo 2026).
- PAdicMIDI — p-adic coherence $\mathrm{Coh}_\pi(p,n)$ on MIDI files; four linked musical visualizations (chromagram, prototype catalogue, inverse system, p-adic tree). Demo includes BWV 1007.
- SEIR-Yucatán — COVID-19 epidemiological modelling (ODEs, complex networks, agents). INDAUTOR registration (2023); archived on Zenodo.
- Magic with p-adic cards — Outreach applet: card trick with N = pk cards, base-p encoding, theatrical flow and mathematical explanation.
Featured publications
Published
Gluing dynamics: ε-precision in solving a non-Archimedean inverse problem
Nopal Coello, V., & Pérez-Buendía, J. R. (2025). Boletín SMM.
Published
Epigenetic forest and flower morphogenesis
Pérez-Buendía, J. R., Cortés-Poza, Y., & Padilla-Longoria, P. (2022).
Published
A Kulikov-type classification theorem for a one parameter family of K3-surfaces over a p-adic field and a good reduction criterion
Pérez-Buendía, J. R. (2019). Annales Math. Québec.
All publications
1.
Accepted (forthcoming)
(2026).
Galois Correspondences for Representations.
Springer — Mathematics in the Caribbean (ICMAM 2025).
2.
Accepted (forthcoming)
(2026).
Dualidad de Stone y espacios profinitos. Una introducción desde la aritmética.
La Gaceta RSME 29(2) (2026).
3.
Accepted (forthcoming)
(2026).
Una interpretación variacional del teorema integral de Cauchy.
Laberintos & Infinitos 57 (2026).
4.
Preprint
(2026).
Rational Interpreters for Discrete Dynamics: Existence, Exactness, and Decomposition over p-adic Fields.
arXiv:2602.05433 (2026).
5.
Published
(2026).
A p-adic reaction-diffusion model of branching coral growth and calcification dynamics.
J. Math. Biol. 92(2) (2026).
Recent talks and conferences
p-adic numbers as a multiscale observation lens — IIMAS–UNAM Yucatán seminar
Seminar on p-adic and profinite geometry for hierarchical multiscale dynamics, with examples in biology and music. 24 April 2026, 12:00–13:00.
Geometry of hierarchy — FMAT–CIMAT Colloquium (22 April 2026)
Colloquium talk, Wednesday 22 April 2026, 11:00 local time. Title: Geometry of hierarchy. Slides and full abstract on the Spanish page.
"How do multiplication tables look?" — Sierra Papacal primary school (2026)
Outreach talk *How do multiplication tables look? Curiosities and secrets of algebra and geometry* at Sierra Papacal primary school, 20 March 2026.
From preimage trees to modular dynamics — CIMAT Mathematics showcase 2026
Talk at the CIMAT-Mérida Mathematics showcase, 27 February 2026, 9:30–10:30. Arithmetic dynamics via preimage trees, Galois action, and modular reduction.
Hierarchical dynamics in genetic regulatory networks via p-adic rational approximations — LVIII SMM 2025
Talk at the LVIII SMM National Congress (2025), Conexiones p-ádicas session. Title aligned with SMM speaker certificate.
Dynamic Topoi and Temporal Sites: A Categorical Framework for Arithmetic Dynamics — LVIII SMM 2025
Talk at the LVIII National Congress of the Mexican Mathematical Society (2025), Number Theory area.
ARQUIBIO 2024 — Tercer Encuentro de Biología Matemática y Métodos no Arquimedianos
Tercer Encuentro de Biología Matemática y Métodos no Arquimedianos. Modalidad híbrida.
GEOTOP-A 2024 — International Conference on Applications of Geometry and Topology
Co-organizer; session chair for Application of Geometry and Topology to Biology. No talk in the program. 8–13 January 2024.
Teaching and mentoring
I teach graduate courses at CIMAT and UNAM on topics in algebraic geometry, condensed mathematics, p-adic dynamics and elliptic curves. I have supervised students at the undergraduate, master’s and doctoral levels.
| Completed | In progress | |
|---|---|---|
| Ph.D. | — | 2 |
| M.Sc. | 5 | — |
| B.Sc. | 2 | — |
| Postdocs | 2 | — |
Blog and essays
Links
FMAT–CIMAT Colloquium 2026 (co-organizer) · Research groups | Projects | Research topics | Outreach | YouTube channel | Substack