P-ADAGIO
Mission
To develop frontier p-adic and non-archimedean mathematics —in number theory, arithmetic geometry, and dynamical systems— and translate its methods towards open problems in natural sciences and philosophy of science, training researchers with structural vision and conceptual rigor.
Objectives
- Original research in geometry of p-adic spaces, Galois representations, and dynamics over ultrametric fields.
- Interdisciplinary applications: p-adic modeling of gene regulatory networks, morphogenesis, mathematical biology, and physics.
- Human resources training: supervision of PhD and master’s theses, postdoctoral stays, and undergraduate research programs.
- Outreach and dissemination: summer schools, graduate courses, and open-access publications.
- Multi-institutional collaboration: CIMAT, UNAM, IIMAS, and international institutions.
Research Lines
- p-adic arithmetic geometry — K3 surfaces, Fargues-Fontaine curve, p-adic Hodge theory, cohomologies.
- Galois representations — arboreal and p-adic representations, good reduction criteria, Galois correspondences.
- Arithmetic dynamics — dynamics over local fields, p-adic preimage trees, modular dynamics.
- p-adic methods in biology — p-adic models of gene regulatory networks, reaction-diffusion on ultrametric spaces, morphogenesis.
- Foundations and philosophy — condensed mathematics, toposes and dynamics, non-archimedean structures in science.
Group Description
P-ADAGIO is a research group dedicated to the study and development of p-adic and non-archimedean methods in arithmetic geometry, algebra, and dynamical systems, and to their intersections with the natural sciences and structural thought.
Our approach begins from mathematical rigor —in particular from the geometry of p-adic spaces, Galois representations, and dynamics defined over ultrametric fields— and extends to applied contexts in physics, chemistry, biology, genetics, and also toward the foundations of philosophy of science.
We conceive mathematics as a language capable of modeling not only the quantifiable, but also the profound: the discrete, the irregular, the ramified. We explore structures that do not follow the traditional measure, because —for us— life itself is non-archimedean.
Team Members
Founder and academic lead:
- Dr. Jesús Rogelio Pérez Buendía — SECIHTI / CIMAT, Mérida Unit. Arithmetic geometry, Galois representations, p-adic dynamics.
Collaborating researchers:
- Dr. Víctor Nopal Coello — CIMAT. Non-archimedean dynamical systems, mathematical biology, p-adic gene regulatory networks.
- Dr. Ángela Fuquén Tibatá — IIMAS, UNAM / CIMAT Mérida. p-adic models of coral morphogenesis.
- Dr. Yuriria Cortés Poza — IIMAS, UNAM. Mathematical modeling in biology and epidemiology.
PhD students:
- M.Sc. Jorge Robles Hernández — PhD in Mathematics, CIMAT. Topologies on the period ring B_dR.
- M.Sc. Luis Manuel Reyes de la Luz — PhD in Mathematical Sciences, FC-UNAM. Galois correspondence in period rings and the Fargues-Fontaine curve.
Group Output
Publications, conferences, and events tagged with P-ADAGIO are listed automatically:
The p-adic tree with graph at the root that appears on the home page is a visualization associated with P-ADAGIO.
Interested in joining P-ADAGIO?
If you wish to join as a collaborating researcher, carry out your thesis, or a research stay, write to us: rogelio.perez [at] cimat.mx
- Collaborating researcher → subject: P-ADAGIO – Interest as collaborating researcher
- Graduate student → subject: P-ADAGIO – Interest as graduate student (thesis)
- Undergraduate student → subject: P-ADAGIO – Interest as undergraduate student
- Research stay or internship → subject: P-ADAGIO – Research stay or scientific internship
How to cite P-ADAGIO in articles
Option A (secondary affiliation):
“P-ADAGIO (P-adic Arithmetic, Dynamics And Galois-Informed Observations), multi-institutional research group.”
Option B (acknowledgments):
“Author is affiliated with the P-ADAGIO research group (P-adic Arithmetic, Dynamics And Galois-Informed Observations).”
Option C (Funding/Acknowledgments):
“This work was developed within the P-ADAGIO research group framework (P-adic Arithmetic, Dynamics And Galois-Informed Observations), CIMAT Mérida Unit / SECIHTI.”
