## European Study Groups with Industry at 40 Years

**March 21, 2009**

Monitoring traffic flow on the A5 motorway between Lisbon and Cascais. BRISA, 60th ESGI, Lisbon, 2007.

**Pedro Freitas**

What do tyre recycling, incubation of penguin eggs, LEGO, and traffic monitoring have in common? If your answer includes a complicated multidisciplinary theory involving female penguins traveling an Antarctic highway in LEGO vehicles with recycled tyres, you are way off the mark. These and a host of other disparate problems, including consumer behaviour, artificial heart pumps, and flight simulators, share the distinction of having been presented in the last few years by industrial partners at European Study Group with Industry (ESGI) workshops in Denmark, the Netherlands, Portugal, and the UK. In short, the common denominator is mathematics.

ESGIs originated in the UK in 1968, under the name Oxford Study Groups with Industry. Since then, the concept has been adopted by other countries, including those mentioned above, and study groups have become a well-established institution and the leading format for interaction between mathematics and industry in Europe. Besides being a source of interesting new problems in mathematics, they also serve as an important mechanism for the transfer of mathematical technology between academia and industry. A list of ESGIs, past and upcoming, can be found in [4].

**How Do ESGIs Work?**A study group normally takes the best part of a week, starting on Monday morning with presentations of the industrial problems to be considered and finishing on Friday morning with the presentation of results by participating mathematicians. A lot of brainstorming, modelling, experimenting, and discussion goes on in the interim, from early in the morning till well after dinner each day. Not to mention, of course, the development and use of a wide range of mathematical techniques.

A typical study group addresses between three and six problems, each presented by a representative of the firm submitting it. The presentation consists of a brief summary of the company's expertise in the area, and a full description of the problem, including solution approaches already attempted. The precise aim should be specified as clearly as possible, together with all relevant information available. A short written summary of the problem should have been sent to the organizers beforehand, giving them time to contact experts in specific areas if necessary. Because it is not realistic to establish a confidentiality agreement, sensitive data should not be given explicitly at this stage; for problems involving sensitive information, firms should provide mock data for use during the workshop. The firms receive written reports later on.

**What Can Companies Expect, and Why Should They Participate?**Study groups are exploratory meetings. Except in very specific cases, it is too optimistic to expect a ready-to-use, thoroughly wrapped up solution from a five-day workshop. This is particularly true when, for example, what is at stake is not a specific problem but rather the launch of a project, or when implementing a particular algorithm requires the production of software. Sometimes, it is simply not physically possible for technical reasons to finish the work in the available time. One of the problems presented by Biosafe in 2008 at the 65th ESGI in Porto illustrates the latter case. Solution of the problem required numerical simulations of the Navier�Stokes equations that, by themselves and with the means available, would have taken longer than the workshop. These simulations were carried out after the meeting, however, and the results were included in the report eventually sent to the firm.

In general, a company has sufficient information by the end of a study group to decide whether it is ready to pick up and proceed on its own, or whether it would be advantageous to establish a more lasting association with one or more of the participating mathematicians.

A point that should be stressed is that most firms, particularly smaller ones, cannot maintain the human resources that would be necessary to address all the specific problems that could arise at some point in their operations. In this sense, study groups can be seen as providing small and medium-sized firms with access to specialized knowledge otherwise out of reach to them.

After the Porto meeting, the three participating companies were asked to comment on different aspects of the process. All agreed that the meeting had been fruitful. Of the three, two had provided a single problem each (the most common scenario), and the other firm had provided two; the firms intended to apply workshop results to at least two of the problems.

**What Can Mathematicians Expect, and Why Should They Participate?**

The mathematics needed for problems arising in study groups varies widely in type, depth, difficulty, and originality. It is possible, for instance, that once a problem has been translated into mathematical form, the mathematics itself will turn out to be trivial. This is normally not the case, however, and industrial problems are more and more a source of challenging new situations that draw on many aspects of (to use the traditional labels) pure and applied mathematics.

With some problems, such as those involving statistics, mathematicians can gain access to data for testing methods and algorithms that would otherwise be difficult to come by. Another important issue is that con-tact with industrial problems keeps mathematicians up to date on challenges facing engineers and other professionals whose university training includes mathematics.

Beyond the obvious benefits, participating mathematicians acquire a wide range of fresh examples of many of the fundamental concepts taught in first- and second-year linear algebra and calculus courses. Checking the fuel level in an airplane tank gives rise to a continuous, non-differentiable function; use of this example allows teachers to make the point that such problems do arise in the real world, without jeopardising mathematical rigour. Methods for describing and dealing with such functions in practical terms are not obvious and, in fact, were the problem posed by Airbus at the 56th ESGI in Bath (2005). A fairly comprehensive collection of ESGI reports on this and other problems is available at the study group Web site [10].

**Getting Study Groups Started**From its beginnings in Oxford, the study group formula has proved successful. It is not always easy, however, to introduce the concept in a country and get the workshops running in a sustainable way. Difficulties, arising on both the academic and the industrial sides, depend on factors more or less known within a country: the tradition of research in industry, for example, and relations between the academic and industrial sectors. The three issues briefly discussed in the following paragraphs reflect the Portuguese experience in introducing ESGI workshops; the three accompanying illustrations are drawn from study groups held in Portugal. The hope is that these experiences will be helpful to people in any country embarking on such an enterprise.

One of the main challenges is to persuade potential industrial partners that they have something to gain by participating in study groups and by building connections to academia. This is an understanding that needs to be built over time, preferably with the help of people who have experience with study groups. In general, it should not be difficult to get members of the international industrial mathematics community to participate, particularly if interesting industrial problems have been obtained. In the Portuguese case, for instance, we were able to count on the collaboration of several British specialists.

On the academic side, some mathematicians might hesitate to become active participants on the grounds that working on such problems does not lead to publications in journals. Although this might be true in the case of problems that can be solved by a trivial application of already existing mathematical techniques, several traditional journals publish results of research originating in interesting study group problems. In fact, the Fields Institute recently created the series Mathematics in Industry Case Studies (MICS) expressly for the publication of study group reports [6].

*Understanding how a Stewart platform functions. FunZone Villages, 60th ESGI, Lisbon, 2007*.

Finally, it might be useful to hold a training session or even one of the quite successful ECMI Modelling Weeks prior to a study group workshop itself. This can be a way to attract students from everywhere in Europe to the study group, and it can give prospective participants a very good idea of the way the workshop will function.

*Numerical simulation for the problem of cooling a tyre-shredding rotor. Biosafe, 65th ESGI, Porto, 2008.*

**Industrial Mathematics in Europe**Anyone who has participated in a study group knows that it can be great intellectual fun. If they are to become a sustainable activity and to have a lasting positive effect on the relation between mathematics and industry, however, study groups should not exist in isolation from other academic activities. Study groups are mentioned in the 2008 Organization for Economic Co-operation and Development Report on Mathematics in Industry [9], but as just one of several recommended mechanisms for promoting partnerships between these two sectors. In fact, irrespective of their success, it is only when integrated into other programmes that study groups will have a lasting positive influence on both mathematics and industry. Such programmes, most of which are mentioned in the OECD report, include:

- Local structures, preferably at the national level, and partnerships between countries: Already well developed in the UK, the Netherlands, Denmark, and other countries, such structures link departments and institutes involved in industrial mathematics, encouraging the sharing of experiences and the creation of networks that help to sustain study groups and attract participants. Such structures facilitate contact between researchers and students working in industrial mathematics and provide visibility for the university industrial mathematics community.
- Second- and third-cycle courses in industrial mathematics: Such degrees (at the post-baccalaureate and PhD levels, respectively) must require a very solid foundation in mathematics, but they should also serve to acquaint students with real-world applications from an early stage. In particular, students should be involved in hands-on activities, of which study groups are but one aspect. Related activities include intern-ships in firms completed as part of a project or thesis; MITACS in Canada has been a pioneer in creating such internships [7].

Apart from putting students in contact with real-world applications, the connection between a degree in mathematics and prospective employers might also help to increase the number of students applying for these programmes, at a time when such growth might become critical for the existence of sustained second and third cycles in mathematics and related areas. Placing mathematics graduates in such positions has an additional obvious advantage--the potential to facilitate communication between academic and industrial mathematicians.

Development of a model for a European master programme in industrial mathematics is under way; plans will be discussed and disseminated in September 2009 at a conference at TU Dresden [1]. Such a programme has the potential to become a driving force for the establishment of industrial mathematics as a standard part of university curricula in Europe. - Invited chairs in industrial mathematics: There is much to be gained from having non-academic practitioners share their research experiences with students and academic researchers. Funding for these positions could come from universities, firms, or even scientific foundations.
- Knowledge-transfer networks: To systematically reach industrial partners who might be interested in collaborating with academia is a nontrivial task, requiring a lot of time and experience. Without the existence of full-time technology translators, promoting these and similar initiatives within industry is very difficult. Such a system is already in place in some countries, including the UK [5].
- Research institutes: The human resources available at the university departmental level could not possibly be sufficient for the development of long-term projects with industry on a sustainable basis. Accordingly, institutes associated with university departments have been established in several European countries; among them are the Fraunhofer Institute [2] in Germany, the Fraunhofer-Chalmers Research Centre in Industrial Mathematics [3] at Chalmers University in Sweden, and the Oxford Centre for Industrial and Applied Mathematics [8] in the UK. Along with their obvious advantages, successful institutes of this type can dramatically increase awareness of the usefulness of mathematics in today's world, among the general public as well as in industry.

**Acknowledgments**A more local version of this article, written in response to an invitation from the Interna-tional Centre for Mathematics (CIM, http://www.cim.pt) for an article reflecting the Portuguese experience, appeared in the December 2008 issue of the CIM Bulletin. I thank the president of CIM, J.F. Rodrigues, for permission to use that article as a starting point for the version that appears here.

**References**

[1] ECMI dissemination conference, "European Master Programme in Industrial Mathematics," September 10�11, 2009, TU Dresden, Germany; http://EMP-IM-2009.tu-dresden.de.

[2] Fraunhofer Institut Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany; http://www.itwm.fraunhofer.de/.

[3] Fraunhofer-Chalmers Centre, Gotemburg, Sweden; http://www.fcc.chalmers.se/.

[4] International Study Groups Web site, http://www.maths-in-industry.org/.

[5] Knowledge Transfer Network for Industrial Mathematics, http://maths.globalwatchonline.com/epicentric portal/site/IMS/?mode=0.

[6] http://www.micsjournal.ca/.

[7] MITACS, Canada; http://www.mitacs.ca/.

[8] Oxford Centre for Industrial and Applied Mathematics, UK; http://www2.maths.ox.ac.uk/ociam/.

[9] Organization for Economic Co-operation and Development, Global Science Forum, Report on Mathematics in Industry, July 2008; http://www.oecd.org/dataoecd/47/1/41019441.pdf.

[10] Study group reports, http://www.maths-in-industry.org/index.html.

*Pedro Freitas is a professor in the Department of Mathematics, Faculdade de Motricidade Humana (TU Lisbon), and a researcher in the Group of Mathematical Physics at the University of Lisbon.*