2005 Hall Medal citation

Bulletin of the Institute of Combinatorics and its Applications, May 2006, pp. 12–14

We have known Jonathan Jedwab for almost fifteen years, meeting him regularly at many conferences. His talks have been consistently excellent; indeed, it was always a pleasure to attend his lectures which can only be described as highly polished, combining depth with clarity and elegance in an extremely successful manner. Therefore, as a coorganizer the first nominator invited him to give plenary talks at three conferences, namely two Oberwolfach meetings (Codes and Designs in 1998 and Finite Geometries in 2001) and the 2001 Capri conference on Discrete Mathematics and its Industrial Applications. We have also followed his publications closely, since we share many research interests.

Dr. Jedwab is no doubt one of the outstanding figures in Design Theory today, where he has continuously considered really hard problems. Sadly, as in Graph Theory, it is quite possible to produce lots of routine papers in Design Theory, in particular in the purely combinatorial parts. In contrast, Jonathan Jedwab's research always concerned topics like difference sets which form a central and truly difficult part of Discrete Mathematics, requiring familiarity with techniques from Geometry, Combinatorial Theory, Group Theory, Representation Theory and Algebraic Number Theory; and it is, of course, also closely related to some important applied areas, in particular to Coding Theory and Signal Processing. Indeed, his joint paper with Jim Davis in JCTA 80 (1997) “A unifying construction for difference sets” can hardly be overestimated in its importance for Algebraic Design Theory. Let us be a bit more specific here. This paper is one of the most important ones in the general area of difference sets ever. To mention just the most striking results:

When the difference set community (and it should be noted that this includes — via the correspondence to sequences and arrays with good correlation properties — also researchers from electrical engineering) first learned about the paper, it created universal excitement. E.g., the first nominator immediately decided to rewrite the new difference sets chapter for the second edition of his “Design Theory” (jointly with T. Beth and H. Lenz, this appeared in the “Encyclopaedia of Mathematics” series of Cambridge University Press in August 1999) to include the new Davis-Jedwab theory of building sets. The paper has become an instant classic and has already had enormous influence. Chen's new constructions have to be seen in this framework, and Ionin's important construction method for symmetric designs (which has yielded many new infinite families) heavily relies on the Davis-Jedwab theory of building sets. Similarly, there have been quite a few follow-up papers concerned with semi-regular relative difference sets.

We would also like to emphasize that the unification paper is not an isolated achievement in Jedwab's career, but is a particular highlight in continuous work of exceptional quality. Let us mention just five more examples:

In our opinion Dr. Jedwab (who is now, after a long period as a senior scientist at Hewlett Packard Labs in Bristol an Associate Professor of Mathematics at Simon Fraser University) is one of the few mathematicians whose work combines theoretical research of the highest quality and originality with important real world applications. It should also be stressed that creativity and originality alone do not suffice to produce a coherent new theory as that given in the unification paper; such a result also requires considerable stamina and perseverance to make the vision become reality.

As this brief description of his work shows, Dr. Jedwab not only has the potential to become an international leader in the broad and important area of Discrete Mathematics and its applications in Computer Science and Engineering, but is already well on his way to this goal. His research shows a consistent quality and depth and has already had a remarkable impact and will no doubt continue to do so. He amply deserves being awarded a 2005 Hall medal.