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Objectives

The COGENT project (standing for Cohomology, Geometry, and Explicit Number Theory) aims to advance the state of the art in an active field at the intersection of algebra, geometry, and computer science. It seeks to promote innovative approaches to the effective methods underlying long-standing conjectures in number theory. COGENT will expand theoretical knowledge aimed at broadening the scope of computer-aided symbolic and exact computation, with a view to potential industrial applications in diverse fields ranging from cryptography to topological data analysis.

The project’s primary training objective is to train a new generation of young researchers with unique expertise, including high-performance computing in geometry and topology, proof assistance and formalized mathematics, machine learning, and quantum computing techniques.

Research Areas

The COGENT project seeks to address several major challenges at the intersection of mathematics and computer science. Its goal is to gain a better understanding of complex mathematical structures, such as arithmetic groups and the K-theory, by developing new methods capable of overcoming the current limitations of computers. By testing fundamental theories such as the Langlands program and using computational verification to ensure error-free proofs, this project also paves the way for new practical applications, particularly in the field of cryptography for data security.

As part of the project, 10 doctoral dissertations will be funded by the European Union and 3 by the United Kingdom (through UK Research & Innovation).

"Securing this kind of competitive funding will allow us to build and foster a community over the long term, as well as to acquire the equipment needed for high-level training." explains Philippe Elbaz-Vincent, a professor at UGA and the project coordinator.

The Project at a Glance

Truck Driver / Pilot	Université Grenoble Alpes
Partners / Consortium Members	Stichting Vrije Universiteit Amsterdam (VUA) Technical University of Braunschweig (TUB) University of Bordeaux (UBx) University of Galway University of Durham University of Sheffield (UFSD) Colorado State University (CSU) University of Massachusetts (UMASS) University of Michigan University of North Carolina at Greensboro (UNCG) University of Oklahoma ID Quantique (IDQ, Switzerland) MSM Programming (Croatia)
Funding Sources	COGENT is a doctoral network funded by the European Commission under the Marie Skłodowska-Curie Actions (MSCA-DN—Grant Agreement: 101169527) and by UK Research and Innovation (UKRI).
Coordinator	Philippe Elbaz-Vincent, professor at UGA at the Fourier Institute (UGA / CNRS)
Amount of Funding	3 million euros
Project Duration	4 years
Launch Date	December 1, 2024