Validated numerics, rooted in Moore’s interval analysis, uses the arithmetic of real intervals to rigorously bound nonlinear functions and control floating-point errors in computations. These methods extend naturally to higher-dimensional and function spaces, forming the basis of rigorous numerical functional analysis. Combined with set-oriented techniques, validated numerics has enabled computer-assisted proofs to address a variety of problems in dynamical systems. Recent advances in computing, and wider availability of platforms that provide support, have led to a resurgence of research activity in the field of validated numerics (and application to computer-assisted proofs).
This ICMS workshop aims to bring together a group of international experts in the area of validated numerics and its applications:
- to review current progress across different application areas (including computer-assisted proofs that use this methodology);
- to develop a young and diverse group of researchers in this field;
- to identify further open problems for which a validated-numerics approach may be profitably utilised;
- to review and compare different software platforms and to discuss common standard features for further software developments;
- to scope international collaborative research projects and associated funding applications to advance the field in the next 10 – 15 years;
- to establish an international Special Interest Group in Validated Numerics as a focus for further activity in this field.
Programme:
The programme will be expanded over the coming months.
Outline of topics:
- Introductory session focused on reviewing the scientific work from 1965 – 2025
- Validated Numerics: Programming Environments
- Applications
- Short talks by Early Career Researchers
- Common standard features for Validated Numerics environments
- Special Interest Group scoping session
- Open Problems Discussion Session
Participation:
Participation will be by invitation. Please indicate your interest using the ‘register interest’ button at the top of this page.
Sustainability statement: Where food is provided, the ICMS offers an entirely vegetarian menu. Single-use plastics are minimised. Unnecessary printed materials will be avoided. Recommended accommodation is within walking distance of the institute. There are excellent public transport links.
