Saint-Girons V: NumPEx highlights the future of numerical computing at the HPC frontier

The fifth edition of the Saint-Girons Conference took place in Saint-Girons, in the Ariège region of France, from 29 June to 3 July 2026. Building on a conference series that dates back to 1994, Saint-Girons V brought together researchers working at the intersection of high-performance computing, numerical mathematics, scientific applications and computer architectures.

This year’s programme reflected the rapidly evolving HPC landscape. Discussions covered numerical linear and multilinear algebra, numerical optimisation, PDE solvers, AI for scientific computing, HPC for AI, quantum computing, mixed and low-precision computing, randomized algorithms and low-rank approximation. The conference highlighted how advances in algorithms and numerical methods must go hand in hand with developments in hardware and computing architectures.

As part of the programme, Alfredo Buttari (CNRS–IRIT) presented “The NumPEx French PEPR Research Program”, introducing the programme, its objectives and its contribution to the development of the French Exascale software ecosystem. His presentation took place during the conference’s HPC and numerical linear algebra sessions, alongside contributions from leading researchers from academia, research organisations and industry.

The conference provided a particularly relevant setting to present NumPEx. Its focus on the interaction between algorithms, applications and computing architectures closely mirrors one of the central challenges of the transition towards Exascale: developing software and numerical methods capable of fully exploiting increasingly

Saint-Girons V also provided a broader perspective on the transformations underway in scientific computing. The rise of AI and massive data processing, the emergence of quantum computing and the move towards new precision regimes are opening new research directions while raising fundamental questions about performance, portability, energy efficiency and numerical reliability.

For NumPEx, these discussions contribute to the wider effort to anticipate the software challenges of the Exascale era, foster connections between the different communities involved in scientific computing and support the development of innovative numerical methods and software.

Beyond the scientific programme, the conference’s informal format encouraged exchanges between researchers and helped create new opportunities for collaboration — a long-standing feature of the Saint-Girons meetings.