James works in what is now perceived to be the frontier between Mathematics and Computer Science. Special areas include Computer Algebra and Cryptography, but also manages High-Performance Computers
Computer Algebra is the science of getting computers to do mathematical problems. The first applications were in differentiation. My original work was in integration, and in proving that integrals cannot be simplified, and I still work there. I have also done algorithmic and complexity theoretic research in computational geometry. More recently, I have collaborated with Maplesoft and the University of Western Ontario, as well as the Chinese Academy of Sciences in Chongquing and Macquarie University, in computational real algebraic geometry software, some of which has made its way into the commercial Maple product (and was a REF 2014 Impact CaseStudy), other parts are available for download from Bath, and may require downloads from Western Ontario as well. Wrestling with this software complexity, and EPSRC’s requirements for publication of research data, has been an interesting exercise, and I would like to see this process streamlined, and more support given to researchers, and am trying to do that at the University of Bath.
I am also involved in the OpenMath project, producing vendor-neutral framework for exchanging complicated mathematical semantics, and this has made its way into MathML 3, and hence into HTML 5. Again, there are interesting challenges integrating this into commercial products as well. The OpenMath project is unfunded, and hence a challenge in sustainability.
Check out contributions by and mentions of James Harold Davenport on www.software.ac.uk