Validated Numerics for Computer-Assisted Proofs

6-10 July 2026, ICMS, Bayes Centre, Edinburgh

Overview

Scientific Organisers

Andrew Burbanks, University of Portsmouth
Ben Mestel, The Open University (retired)
Mark Pollicott, University of Warwick
Julia Slipantschuk, University of Bayreuth

About the Workshop

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 mathematicians at all career stages 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.

Themes

The history and development of validated numerics and computer-assisted proofs
Developing early career researchers
Programming environments and common standard features for validated numerics
Potential for a Special Interest Group in Validated Numerics
Applications
Open Problems

Participation

Participation is by invitation. Please indicate your interest using the button provided at the top of the ICMS page. Accommodation and lunches are provided for invited participants on the main workshop days. Limited support is available to assist with transport.

Resources

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.

Sponsors and Funders

The workshop is supported by the International Centre for Mathematical Sciences (ICMS), Edinburgh, via Workshop Grant 2416-BUR, the London Mathematical Society (LMS) via the Scheme 1 Conference Grant 12502, and the Glasgow Mathematical Journal Trust (GMJT) via the GMJT ICMS Block Grant 2026/2027.

ICMS LMS GMJT

The ICMS is supported by the Engineering and Physical Sciences Research Council (EPSRC), Heriot Watt University, and the University of Edinburgh.

EPSRC Heriot Watt University University of Edinburgh