Research | Rogelio Pérez Buendía

Research

My work revolves around arithmetic geometry and p-adic methods, as a unifying thread linking p-adic Hodge theory, Galois representations, rigid and logarithmic geometry, Berkovich spaces, and affine lines in pure mathematics.

The core of my research articulates arithmetic geometry and arithmetic dynamics. On the dynamical side I study iteration and the structure of maps in non-Archimedean settings (p-adic and related), as well as over finite fields, congruence rings, groups, and the algebraic-geometric objects arising in those contexts. This set of research lines has its own mathematical motivation. The applications – including systems biomathematics, cryptography, and other links to applied science – constitute in addition a selective use of those ideas and techniques; they do not by themselves define the scope of the programme.

Research lines

Each topic links to a page with a description, illustrations, and cross-references to publications, courses, and talks.

Topic
Arithmetic geometry	View
Algebraic geometry	View
Number theory	View
p-adic geometry (Berkovich)	View
p-adic cohomologies and Hodge theory	View
Logarithmic geometry	View
Arithmetic dynamical systems	View
Arithmetic dynamics	View
Non-Archimedean dynamics	View
Condensed dynamics	View
Condensed mathematics	View
Commutative algebra	View
Cryptography and coding theory	View
Biomathematics	View

Working groups and initiatives

Participation in multi-institutional research groups and initiatives. I collaborate with the biomathematics group at IIMAS-UNAM developing p-adic models for gene regulatory networks and morphogenetic patterns in living organisms.

P-ADAGIO

P-adic Arithmetic, Dynamics And Galois-Informed Observations

A multi-institutional research group devoted 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 thinking. Founder: J. R. Perez Buendia.

Go to the P-ADAGIO page

Frontier Project – Unconventional Models for Biology

Grant: CF 2019/217367 (CONAHCyT, 2019–2025). Unconventional mathematical and computational models for the study and analysis of relevant problems in Biology. Technical co-PI: J. R. Perez Buendia (CIMAT Merida) and Dr. Yuriria Cortes Poza (IIMAS-UNAM).

Go to the Frontier Project page

CONAHCyT Chair Merida–CIMAT

Project 779: Strengthening mathematical and scientific computing capacities in the State of Yucatan. Research, human resource training and outreach within the Researchers for Mexico programme, at CIMAT Merida Unit.

Go to the Chair page

Featured publications

Published