Mathematical Problems in Industry Workshop Celebrates 25 Years

April 1, 2010

Louis F. Rossi

The Mathematical Problems in Industry workshop celebrated its 25th anniversary last summer at the University of Delaware and will convene for the 26th time this June at Rensselaer Polytechnic Institute. The MPI workshop carries on a tradition that dates back to 1968, when Oxford professors Alan Tayler, Leslie Fox, and John Ockendon had the idea of hosting a study group focused on contemporary problems. What set that first workshop apart from other mathematical workshops was that the organizers sought out problems from outside the academy. The structure of the workshop was simple: Presenters would bring good mathematical problems, and participants would spend the vast majority of the time in break-out groups working on the problems. The math-in-industry workshop concept, born from that simple initiative, has been successfully replicated, with slight modifications, around the world.*

In the mid-1980s, RPI professors Bob O'Malley, Ash Kapila, and Don Drew attended one of the early Oxford study groups. Hoping to bring a similar workshop to the U.S., O'Malley and Kapila approached the Sloan Foundation for seed money. Julian Cole, also of RPI, played the vital role of building a group of industrial contacts who might present problems at the nascent workshop. In 1985, with support from the Sloan Foundation, RPI hosted the first MPI workshop, and this American industry workshop has been running strong ever since.

Democracy in Problem Solving
Industry workshops have been modified slightly from the original Oxford model, with different themes and audiences, but all share many ingredients. First, participants are united in the common purpose of creating mathematical insights into the presented problems. A workshop is a time to get work done, and the success or failure of the workshop is measured by the progress made on these problems. While results are of primary importance, the workshop provides an exciting educational environment for graduate students, who have the opportunity to see high-quality research done in real time. Historically, graduate students have participated in the workshop at many levels, from performing literature reviews to working alongside faculty in solving problems.

Second, the workshop days are set aside to accomplish this common goal, with the minor exception of a few minutes reserved at the end of each day for quick progress reports. Rather than scheduling speakers and sessions, the organizing committee is responsible mainly for ensuring sufficient space, network access, caffeine, and carbohydrates to make everyone as productive as possible. Few, if any, lectures are given. In their place are lively debates and hard work focused on the workshop problems.

Third, no rules or restrictions are placed on participants, a feature that makes the industry workshop one of the most democratic meetings in existence. All contributions are welcome. One classroom is assigned to each problem, and participants are free to work on the problem(s) of their choice. The atmosphere in a room can vary from the heavy silence of deep concentration to energetic discussions carried out at the chalkboard. It is not uncommon for participants to move from room to room, sharing a few quick ideas and then moving on to other problems. Progress comes in fits and starts, but something good usually gels in the end.

A festive atmosphere prevails on the last day, which is devoted to final presentations and "Coleman balls." (In honor of British sportscaster David Coleman, who was known for his verbal fumbles, participants celebrate notable outbursts that have been surreptitiously recorded during the week. Examples include such gems as "Let's get rid of the plusses and do some actual math" and "I didn't know anything until 2 minutes ago.") Finally, each study group produces a coherent written synopsis of the results achieved for each presented problem.

Drawing in Grad Students
The MPI workshop stands apart from other continuously running industry workshops in two ways. First, no formal organization assumes ownership of the workshop, which is kept alive and well by an informal group of faculty from different institutions. Principal among them is Don Schwendeman of RPI, which has hosted 15 of the 25 MPI workshops held since 1985; other hosts have been the University of Delaware (five workshops, with Rich Braun, David Edwards, and Lou Rossi as local organizers) and Worcester Polytechnic Institute (three workshops, with organizers Joe Fehrbach and Bogdan Vernescu). In the democratic spirit of the meeting, the organizers cooperated to secure a Special Meetings grant from the National Science Foundation for the workshops held in 2008 (at WPI), 2009 (Delaware), and 2010 (RPI). NSF support enabled the organizers to include more early-career mathematicians and to expand their outreach to industrial presenters.

A second distinguishing feature of the MPI workshop is its tight coupling to the Graduate Student Mathematical Modeling Camp. In 2004, recognizing that graduate students participating in MPI would benefit from a gentle introduction to the workshop environment, Schwendeman initiated GSMMC, which is structurally similar to MPI but lasts only four days. The problems are presented by faculty mentors who are experienced modelers and workshop participants. Because it is designed for students, GSMMC emphasizes the process rather than the generation of new mathematics. Most students who attend GSMMC choose to attend MPI in the subsequent week.

The 25th MPI workshop at Delaware focused on five problems from fields as diverse as information technology, materials science, and biophysical modeling. Presenters were Fern Hunt of the National Institute of Standards and Technology, "The Dynamics of a Model of a Computer Protocol"; Uwe Beuscher of Gore & Associates, "Characterization of Porous Media Using Network Models for Filtration Applications"; Ferdinand Hendriks, a modeler at Hitachi Global Storage Technologies, "Homogenization of Self-acting Air Bearing Problems for Patterned Magnetic Recording Media Patterns"; Nowwar Mustafa, a physician at Christiana Care, "Vulnerable Plaque: Can We Predict Which Plaque Will Lead to the Next Adverse Cardiac Event?"; and John Abbott of Corning Incorporated, "Development and Persistence of �Static' or �Dead' Zones in Flows of Certain Materials." One indicator of success in a workshop is broad appeal. For the 25th MPI workshop, close to 60 participants from 26 institutions in the U.S. and U.K. attended, including more than 30 graduate students, many of whom also attended GSMMC.

The critical components of a successful workshop are great problems and great presenters; both are essential. A great problem has a short learning curve, so that the participants can comprehend the issues, and it is accessible enough for the study group to bring in results in a week's time. The problem needs to be suited to the participants: If a problem requires expertise far afield from that of participants, the group risks spending all its time learning the basics. In fact, it is not unusual for organizers to identify and invite participants with special skills to help make the workshop a success.

The presenter needs to be readily accessible during the week; participants routinely make progress only to illuminate new issues that require clarification. Participants commonly spend the first day interrogating the presenter to glean essential details and information as they lay the groundwork for a mathematical model. It is not unusual for a presenter to gather new data for the group or bring in extra supporting materials as the group discovers new issues or requires new assumptions. Presenters need not be mathematically sophisticated, although many are. It is essential, however, that presenters be heavily invested in their problems and any results the study group produces.

With no tangible reward for hosting a workshop, much credit is due to RPI for doing the lion's share of the work for the last 25 years. The organizers of the 25th MPI workshop endowed a perpetual plaque to record workshop sites, with plenty of room for the names of host institutions for the next 25 years. Finally, tipping our hat to MPI's Oxford University origins, we asked Oxford friends to bring something to the U.S. that might travel from host to host. They decided on a silver drinking tankard, which, bearing the inscription "Solutions through acumen and grit," is on display at RPI, the host for the 2010 MPI workshop, ready to move on to its next (yet to be determined) host in June.

Successful Sharing of Ideas
An ongoing debate concerns the purpose industry workshops serve. Is the primary aim to serve faculty and graduate students by introducing them to new problems and new mathematics? Or is it to provide something of immediate commercial value to the presenters?

Experience has taught organizers of the need to avoid confusing relevance and commercial value. Some of the early MPI workshops were designed around the perception that workshops would provide significant commercial value, and that companies should thus be willing to pay a modest fee to present a problem. This has sometimes been the case, sometimes not; despite its success, MPI may never be financially self-sufficient. Math-in-industry workshops are highly heterogeneous, bringing together presenters and participants who measure the value of the meeting in different currencies.

For faculty and graduate students, MPI offers a valuable opportunity to spend a week learning something new without a long-term obligation. The cost is relatively low: There are no registration fees; housing is cheap, and most meals are provided. Workshop activities always yield a non-peer-reviewed workshop report, and sometimes lead to refereed publications, which can help with tenure and promotion. The biggest draw for participants, however, is the sense that people outside the academy care about what happens at the workshop. Without this relevance, faculty and student interest would likely evaporate.

Industry presenters find value in focused attention and rapid progress on their problems. Some are mathematically sophisticated individuals looking for the new perspectives. In the words of Ferdinand Hendriks, a regular presenter at MPI workshops, "There is a tendency to rely upon commercial packages that provide very little insight. Analysis makes us better users of commercial packages." Moreover, MPI can provide essential technical expertise to presenters from companies or agencies that do not have modelers or basic R&D groups. This value is delivered at a cost, however. In addition to the workshop fee, presenters must spend a week away from their regular duties to attend the meeting.

MPI, then, must serve two equal purposes. The workshop must be relevant outside the academy, and it must provide value to faculty and students. Fern Hunt, a first-time presenter at the 25th-anniversary workshop, succinctly characterized the MPI meeting as the "successful sharing of ideas." The workshop is suitable for both purposes, but ideal for neither. However, the industry workshop is a unique and irreplaceable mechanism for bringing these diverse interests together at minimal cost and with maximal benefit to all involved.

The MPI workshop is always open to new participants and new industrial partners. The 26th MPI workshop will be held at Rensselaer Polytechnic Institute, June 14�18, 2010. Travel support is available for young faculty and graduate students. Registration information is available at http://www.rpi.edu/dept/mat/MPIWorkshop/. Graduate students interested in attending GSMMC (June 8�11, 2010, can find more information at http://www.rpi.edu/dept/math/GSMMCamp/; travel support and lodging will be provided to all students accepted into the program.

Louis Rossi is a professor in the Department of Mathematical Sciences at the University of Delaware.

*Related articles have appeared in SIAM News: "Mathematics-in-Industry Study Groups---A Global Phenomenon," October 2007, and "European Study Groups with Industry at 40 Years," March 2009.

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