Viewpoint
A Fortnight in Bellagio
By Anna Nagurney, Patrizia Daniele and Monica Gabriela Cojocaru
From March 10-23, we were in residence at the Rockefeller Foundation's Bellagio Study and Conference Center located in Bellagio on Lake Como in northern Italy. The Bellagio Center opened in 1959 to allow scholars, scientists, artists and writers, as well as policy-makers and practitioners from around the globe, to pursue their research and creative work. Its setting is idyllic with views of Lake Como and the Alps, coupled with magnificent gardens and parks. The beauty of the setting, the support that we received, the rewarding interactions with other scholars outside our disciplines, and the musicians, artists and writers that were in residence during our stay provided us with a truly unique and exceptional environment in which to pursue our research project.
We were the first operations research team in the Center's history. Our project was titled, "Dynamics of Complex Networks in an Environment of Risk and Uncertainty: Theoretical Foundations and Applications to Global Supply Chains and International Financial Networks." Our proposal was submitted in response to a letter of invitation that Anna Nagurney received following her Distinguished Chaired Fulbright in Innsbruck, Austria, in 2002.
While at Bellagio, we stayed at a mini villa set up with access to laptops and Internet connections. Our research interests and backgrounds created an incredible synergy from which we could conduct our research project. Although we had interacted through e-mail, only Patrizia and Anna had ever met face-to-face, but we knew each other through our research interests and publications.
From the first day of our residency, we established a rhythm that enabled us to work intensively from early in the morning until very late at night. In addition, we took part in some memorable intellectual conversations and discussions during the meals as well as the evening seminars. For the most part, we worked together in the conference room of our villa, brainstorming, questioning, connecting, researching the existing literature, marking up the white board with equations and diagrams, and establishing our results. Our primary goal was to build the theoretical foundations through the connections (and unification) of projected dynamical systems and evolutionary variational inequalities on Hilbert spaces. From the former, we could then gain powerful computational procedures, whereas from the latter we could gain a new richness in terms of model development and analysis in operations research/management science, as well as in economics, finance, engineering (notably, transportation science) and environmental sciences.
When the intensity of our research and work necessitated a respite, we would take some time for a meal, a walk or a song; laughter would soon follow. We shared with the artists, musicians, writers, human rights activists, public health experts and historians what we consider to be the beauty of mathematics, its relevance and its special nature in terms of research, creativity and scientific discovery. We found that many of the residents eagerly anticipated our seminar presentation that was unique not only because it was being presented by three females, but by three female operations researchers!
During our presentation, Anna provided the background and foundations, focusing on a spectrum of network-based applications that had been studied as finite-dimensional variational inequality problems and as projected dynamical systems. Anna described applications such as supply chain networks, international financial networks with intermediation, as well as recycling networks (for relevant papers, see http://supernet.som.umass.edu). Patrizia followed with an overview of her modeling work on time-dependent spatial price and financial network models using evolutionary variational inequalities, coupled with her contributions to the existence and uniqueness of the solutions. Monica provided not only a discussion of infinite-dimensional projected dynamical systems, but showed dynamic trajectories using MAPLE. She also discussed why math is important, what is special about math, and listed some of the unsolved problems dating to the 19th century. The three of us then summarized the work that we had accomplished during the residency and highlighted the impact that it might have.
The research team residency was an experience of a lifetime. It demonstrated the rewards of a sustained collaboration in an environment of great beauty and without the obligations of daily life. It was a privilege to be able to partake in the activities of the Bellagio Center during our two-week tenure, and we hope to return to our disciplines what we learned and discovered. Finally, we hope that we helped get across the idea that operations researchers can be very dynamic, social and engaging individuals, with interests that transcend different areas.
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Patrizia Daniele was born in Sicily and received her bachelor's degree at the University of Catania and her doctorate in applied mathematics and computer science from the University of Naples in 2000. She is an associate professor of Operational Research at the University of Catania in Catania, Italy.
Monica Cojocaru was born in Romania and received her bachelor's and master's degrees in mathematics at the University of Bucharest. She received her doctorate in mathematics from Queen's University in Kingston, Canada. She is an assistant professor at the University of Guelph in Guelph, Ontario, Canada.
Anna Nagurney is the John F. Smith Memorial Professor at the Isenberg School of Management at the University of Massachusetts.
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