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John Ball

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John Ball

John Ball

Fellow of the Royal Society of Edinburgh at 32 and Fellow of the Royal Society of London at 41, Sir John Ball was awarded the Theodore von Kármán Prize by the American Society for Industrial and Applied Mathematics in 1999. Today, he is one of the leading global specialists in nonlinear elasticity, the calculus of variations, the mathematical theory of materials and, more generally, applied mathematics.

This honorary doctorate comes in recognition of an exceptional body of work and numerous contributions in the areas of calculus of variations, nonlinear partial differential equations, infinite-dimensional dynamical systems and their applications to nonlinear mechanics.

Which of your research achievements do you feel are most significant, and why?

Like many researchers I tend to be more enthusiastic about my most recent work which today deals with liquid crystals. However, no doubt my contributions were better when I was younger!  My work on nonlinear elasticity which equations were first written down by Cauchy around 1822, established for the first time the existence of energy-minimizing configurations under realistic conditions on the material. We still know very little about these configurations, for example whether they vary smoothly from point to point. In trying, and failing to prove this, I nevertheless found with the late Vic Mizel some surprising one-dimensional examples whose minimizers don’t satisfy the Euler-Lagrange equation. Influenced by Jerry Ericksen, Dick James and I later studied cases when there is no energy minimizer, showing that one could in this way understand microstructures arising from solid phase transformations.  These are pieces of work that I still find very satisfying.


Can you outline your current research interests in the mathematics of liquid crystals?

I am working on different aspects of the Q-tensor theory of liquid crystals, due to the great French scientist Pierre-Gilles de Gennes, which describes the orientational order of rod-like liquid crystal molecules by a tensor order parameter, whereas the commonly used Oseen-Frank theory does so in terms of a vector-field. Surprisingly there has not been much mathematical work on the Q-tensor theory which leads to many unexplored mathematical questions. With Arghir Zarnescu I have been studying the relationship of the theory with that of Oseen-Frank, which has topological aspects, while with Apala Majumdar I have been working on the question of what preserves the physical constraints on the eigenvalues of the Q-tensor. The work concerns basic theoretical issues, but perhaps there will eventually be some practical applications.


Your many distinctions and your roles as past President of the IMU and current chair of the CIEC make you an important spokesman for mathematics internationally. In your opinion, what are the most pressing issues concerning mathematics today at the international level?

One important issue, not just affecting mathematics, is the increasing use of metrics for evaluating research, such as impact factors of journals. This is leading to unethical practices such as impact factor manipulation, and threatens individual researchers for whose assessment such statistics cannot reliably replace peer review. 

The number and quality of training of mathematics students at all levels are continuing concerns, the former being related to a lack of public understanding of mathematics and of its importance for society. Of course mathematical talent does not respect geographical boundaries, and much work needs to be done before the opportunities for developing this talent depend less on where you are born.


Do you feel that there is sufficient interaction between the mathematics community and other disciplines (life sciences, for example), for which mathematics are extremely important? Which structural changes would you propose to further promote such interaction?

As subjects become better understood they become more mathematical – this is one of the reasons why the role of mathematics in the life sciences is increasing. Realistically, increasing the interaction has to be tackled through young people. Young life scientists, for example, need a good mathematical training, at least sufficient to understand the value of mathematical models, while mathematicians need to encounter a broad range of applications in their education, and get some experience of breaking down language barriers between disciplines.


Tell us about your collaboration with François Murat and the Laboratoire Jacques-Louis Lions. How did this research relationship arise? 

One of the first mathematical books I studied as a research student was Quelques méthodes de résolution des problèmes aux limites non linéaires by Jacques-Louis Lions, so I was early on an admirer of the French style of mathematics. Then, shortly after I had proved my existence theorem for nonlinear elasticity, it became clear that the methods were closely related to those of the theory of compensated compactness developed by Luc Tartar and François Murat, so I made a number of visits to the Laboratoire d’Analyse Numerique, as it was then called, including a sabbatical year 1987-88. This was the beginning of my collaboration on the calculus of variations with François, and of a deep and enduring friendship.  Since then I have been a regular visitor to Paris and the Laboratoire Jacques-Louis Lions. 


Mathematics may be the universal language of science and technology, but students and researchers must use other languages to discuss it. How have you dealt with the language barrier while in Paris? Do English language universities and researchers have an unfair advantage when it comes to evaluation?


Fortunately I speak reasonable French, so I have not felt a language barrier. Of course the fact that English is the international scientific language confers some advantage on those for whom English is their native language. Most French mathematicians I have met speak pretty good English and many seminars are in English (especially if foreigners are present), but certainly foreigners who speak French can gain more from a scientific visit to Paris than those who don’t. The very high reputation of French mathematics internationally suggests that the language issue is not much of a problem for the French.


As a highly distinguished British mathematician and academic, how do you view UPMC’s position in the higher education landscape, both at the European and international levels?

There is absolutely no doubt that Paris is the main international centre for the study of partial differential equations, and that the Laboratoire Jacques-Louis Lions is the hub of this activity and one of the very best applied mathematics departments in the world. Of course it is the department of the UPMC that I know the best, but the university is clearly a very important player on the world stage.


What does this honorary degree represent for you? Do you envisage continuing your collaboration with UPMC in the future?

It is moving for me to receive an honorary degree from such a prestigious institution with which I have had such a close and fruitful association over the years. There is no doubt that I will be continuing my collaboration and returning to visit often!