Here is a brief summary of the program:

**David H. Bailey** was a faithful collaborator of Jon Borwein in many papers concerning pi. After recalling the memories that bind him to Jon, he chose to present to the audience a fascinating result related to the Poisson equation of mathematical physics: in 2-D, when the two arguments are rational numbers, the value of the function is 1/pi times the logarithm of an algebraic number. Using an intensive algorithm involving the PSLQ algorithm and very high numerical levels of precision, they discovered and proved a formula which gives the degree of the minimal polynomial for the algebraic number associated with the case (1/s,1/s) for a natural number s.

**Patrick Combettes** knew Jon Borwein about twenty years ago and has maintained a close professional and personal contact with him. In his paper, he addressed a typical Jon theme, namely the unification of a set of problems using nonlinear analysis tools. He showed that convex prospective functions are implicitly present in a wide range of applied mathematical problems. Jon and others have systematically investigated their properties as well as related proximal methods, and have presented applications in the data sciences.

**Ivar Ekeland** has, as usual, brilliantly wrote on the blackboard the central idea of the variational principle of Borwein and Preiss. He has shown that the idea behind the Borwein-Preiss result makes it possible to replace the Lipschitzian perturbations of the Ekeland principle by quadratic perturbations. He concluded his paper by giving an application to the Hartree-Fock equations for Coulomb systems.

**Martin Groitschel** spoke with emotion about the actions he shared and led with Jon Borwein for a significant period of time on the International Committee on Electronic Information and Communication (CEIC) of the International Mathematical Union (IMU), a committee over which Jon presided. In particular, he presented some transparencies, found in his archives, which Jon had used in presentations. The documents produced by the CEIC have had an undeniable influence on development worldwide on these issues.

**Alexander Ioffe** spoke on a number of issues in which Jon Borwein’s contributions have led to substantial developments in variational analysis. For example, he explained the decisive role of the Borwein-Preiss variational principle as well as the Borwein-Fitzpatrick theorem (relating to the sequential compactness) in non-convex sub-differential computation. He also discussed the ideas of Borwein-Moors on the rich families of sub-spaces and their influence on the principle of separable reduction, which is a powerful and effective instrument of analysis in Banach spaces theory. In conclusion, he elaborated on some details of recent developments in the theory of non-smooth transversality, a theory whose development was initially stimulated by the work of Bauschke-Borwein on the linear convergence of the alternative projection method for convex sets.

**Adrian Lewis** was the post-doc of Jon Borwein in Halifax and his colleague at Waterloo. He revived some anecdotes shared with Jon and then returned to the ideas and works of Jon concerning metric regularity, a theory of very high current interest because of numerous applications in different domains, covering both theoretical and algorithmic aspects. Jon was one of the precursors of this concept, of which traces can be found even in the works of Banach, Lusternik and Grave.

**Luc Trouche** recalled the genesis of his collaboration with Jon (three hands: a mathematician and two didacticians) who came out of “Tools and Learning: Instruments for Learning”, a book whose starting point was a study by the International Commission on Mathematical instruction on experimental methods. He then briefly described the numerous interactions on the conditions of transposition of “experimental mathematics” for the “ordinary” teaching of mathematics and recalled that these studies, abruptly interrupted by the death of Jon, have opened many tracks that are still being explored.

**Jim Zhu** was a postdoctoral fellow at Jon University at Simon Fraser University in Vancouver. Since then he has been one of his loyal collaborators and has benefited from his advice and ideas. Shortly before the unexpected death of Jon, they had developed a project on the role of maximization of entropy in several fundamental results of mathematical finance. In his paper, Jim gave examples of the theorems of the two mutual funds for efficient portfolios in the sense of Markowitz in the capital asset pricing model (CAPM), the fundamental asset valuation theorem, the selection of a martingale measure to evaluate contingent assets in an incomplete market, and the calculation of upper and lower limits of coverage. Jon had the idea that the theorem of the two mutual funds could be understood as deriving from a problem of maximization of entropy and that this structure should be found in other problems of mathematical finance. Jim concluded his presentation by saying that sadly Jon could not see the accomplishment of this project.

Finally, the organizer Michel Thera invited two young researchers, Francisco J. Aragon Artaacho and Matthew Tam, who were respectively the last post-doctoral and doctoral candidates of Jon Borwein:

**Francisco J. Aragon Artacho** gave a presentation on a project he led in Newcastle with Jon Borwein, with the evocative title “Walking on real numbers with Dr. Pi”. He described various tools for the representation of floating-point numbers as a random walk in the plane, in order to measure the randomness of the digits. Thanks to the influence of Jon Borwein, this work received considerable attention in the mainstream press. In addition, he illustrated the fact that the Douglas-Rachford algorithm could be used to solve the problem of coloring graphs.

**Matthew Tam** gave a presentation based on the different results he shared with Jon Borwein and thus contained a mix of optimization techniques, experimental mathematics and visualization. In particular, he presented the development of a version of the Douglas-Rachford algorithm for convex feasibility in the presence of several sets and its application to the determination of protein conformations.

Two different groups sent special messages to be read at the conference:

**Message from Fatiha Alabau, President of SMAI:**

The french learned society SMAI would like to express its profound admiration for the work and the scientific personnality of Jonathan Michael Borwein and would also like his family to be assured that the thoughts of the applied mathematical French community are with her on this particular day.

**Message from the University of Newcastle:**

From all of us in Newcastle who, while a hemisphere away, are united with you in paying tribute to our friend and colleague Jonathan M. Borwein. Jon first visited Australia, and the University of Newcastle in particular, in the mid 80’s; the first of numerous short and mid term visits. So he was no stranger to us when in January 2008 he, together with his wonderful wife Judi, two of his three daughters; Naomi and Tova, and grandson Jacob, moved to Newcastle to become Laureate Professor of Mathematics. Jon’s impact on mathematics at Newcastle and more generally Australia was both immediate and profound. Within months he had established the Priority Research Centre for Computer Assisted Research Mathematics and its Application (CARMA) and actively engaged with the Australian mathematical community assuming various roles in the Australian Mathematical Society, Australian Mathematical Sciences Institute and soon as an elected member of the Australian Academy of Sciences. Jon was a unique and amazing colleague. His personality and love of scholarship were infectious, and equalled only by his enjoyment of good company and a good debate. His sense of fairness and the easy generosity with which he shared his great knowledge, insightfulness and creativity made Jon an outstanding mentor and the best and most natural of collaborators. And, for many of us a close and much valued friend. We thank you all for the honour you bestowing on Jon today. It is a day of profound sadness, but also a celebration of the great privilege of having known and in so many cases worked with him. Jon has left us with an indelible legacy, but also a great void. We miss him more and more with every passing day.