ANID Exploration 13220060

Welcome to the webpage of the

ANID Exploration Project 13220060

2023-2025

The PDE approach in two monster number theory problems

Funded by ANID Exploration, Center for Mathematical Modeling CMM, and ANID Fondecyt

News: Scientific report 2022-2025 first version (in Spanish)

Since December 19, 2025, ANID Exploration Project 13220060 will no longer be continued.

However, new research will come out soon in terms of new projects.

We acknowledge ANID for the support during this 3-year period.

Instructivo Informe Académico Final Concurso Exploracion 2022 (1).docx - Google Docs.pdf

This project, mainly funded by ANID, aims to open new paths in the study of two highly recognized open problems in Number Theory, seen this time from the point of view of Partial Differential Equations (PDEs). Our motivation is to give new methods and ideas that may clarify some intriguing aspects of these problems, and in a near future, to provide a new area of knowledge for PDE and Number Theory researchers.

The two problems that we are seeking to describe in this 3-years project are PDE motivated versions of the Riemann and Collatz conjectures. By working on these problems we propose the creation of bridges between Number Theory and PDEs researchers and new methods which will be generalizations of PDE techniques. New models will be also defined by this project, and studied in detail by young researchers.

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