DIMACS Center, CoRE Building, Rutgers University

**Organizers:****Alejandro Adem**, Pacific Institute for the Mathematical Sciences (PIMS)**Russell Caflisch**, Institute for Pure and Applied Mathematics (IPAM)**Lou Gross**, National Institute for Mathematical and Biological Synthesis (NIMBios)**Iain Johnston**, Chair of MPS Advisory Committee to NSF**Simon Levin**, coAuthor of Toward a Science of Sustainability**Fred Roberts**, the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)**Christiane Rousseau**, Centre de Recherches Mathematique (CRM) and Chair of program Mathematics of Planet Earth, a joint program of 14 North American mathematical sciences institutes)**Richard Smith**, Statistical and Applied Mathematical Sciences Institute (SAMSI)

The project is a joint activity of six mathematical sciences research institutes, four in the US and two in Canada, namely IPAM (Institute for Pure and Applied Mathematics), NIMBios (National Institute for Mathematical and Biological Synthesis), SAMSI (Statistical and Applied Mathematical Sciences Institute) and DIMACS (the Center for Discrete Mathematics and Theoretical Computer Science) in the US and CRM (Centre de Recherches Mathematiques) and PIMS (Pacific Institute for the Mathematical Sciences) in Canada.

The growing human population and increasing pressures for development have led to a variety of challenges for life on our planet, in particular whether current patterns of human activity are sustainable. Human activity is closely tied to the natural environment and there is a two-way interconnection between human activity and environmental processes. Increasingly, we are noting how human activities affect the systems that sustain life, including climate, healthy air and water, availability of food. The earth has finite resources that we need to sustain our life style: sources of energy, clean water, arable land. As environmental conditions change, there are possibilities for new diseases, species can move into areas to which they are non-native and crowd out the species to which we are accustomed, and the human condition can be threatened by environmental change. Fundamental societal structures such as national boundaries and the health of our economic systems can be affected by competition for changing natural resources, shortages and in some cases surpluses. These problems are complex, multi-disciplinary, and intertwined. They call for a "science of sustainability."

Recognizing the challenges to life on our planet as we know it, NSF has initiated a major new initiative on sustainability (SEES) that involves all directorates in the Foundation. However, to date, the mathematical sciences have been involved only in a limited way. Yet, there are many mathematical problems of great complexity, interest, and importance in a wide variety of areas that it would be important to get the mathematical sciences community to work on. This workshop seeks to describe these mathematical challenges and will lead to a report to be circulated widely to the mathematical sciences community as well as NSF and also its counterpart in Canada, NSERC. The problems of sustainability cross many disciplines. The mathematical challenges the project identifies can be expected to lead to research on a wide variety of topics of great societal importance such as climate change, environmental health, management of limited natural resources, and the interconnections of these topics with healthy economic systems and enduring social structures.

**Addendum**

Our workshop will not be organized in the usual way, with lectures, panels, etc. Instead, we are asking leaders in the mathematical sciences community and scientists working in substantive areas that are amenable to mathematical analysis to prepare white papers in advance that will be read by all the participants (participants to be chosen by invitation). There will be four topics for white papers. At the conference, focus groups in each topic will meet and develop agendas for future research, starting discussion around the white papers. A member of each focus group will be asked to write up the discussions and also present them to the entire workshop in a plenary session. We expect to produce a report that will be given widespread circulation both to NSF and NSERC and to the mathematical sciences community.

**Workshop Themes**
(The following theme descriptions borrow heavily from the report "Towards a Science of Sustainability")

**Theme 1: Human Well-being and the Natural Environment**

Under this theme, we seek to identify a small set of research challenges in the mathematical sciences where progress could advance our understanding of the interdependence of human well-being and the natural environment. Understanding this interdependence is an essential foundation for sustainability science. Under this theme, we will focus on developing an internally consistent mathematical sciences-based framework for showing how use, and even depletion, of aspects of the natural environment could be consistent with sustainability so long as they are converted into other forms of capital (e.g. manufactured, human, social) at appropriate rates capable of maintaining human well-being over the long-term. Key issues for sustainable development involve precise definitions of human well-being, and mathematical models of how natural capital contributes to human well-being, how human actions impact on natural capital, tradeoffs in benefits over space (intra-generational equity) and time (intergenerational equity), and the role of institutions, technology and knowledge in promoting sustainable development. Health (and freedom from disease) is one sample component of sustainability and of interest here, among other things, is the potential for emerging infectious diseases to arise from climate change and greatly impact both human and natural systems. Mathematical epidemiological methods, linked to climate change, provide a growing area of research which should be linked with sustainability science.

**Theme 2: Human-Environment Systems as Complex Adaptive Systems**

Under this theme, we will focus on the dynamics, both endogenous and in response to outside disturbance, of coupled Human-Environment Systems (HES). Key questions regarding the dynamics of HESs relate to the ways in which their behaviors emerge from adaptive actions by their constituent agents, interacting across multiple scales. Addressing such questions will require new mathematics-based theories that must merge holistic and reductionistic perspectives, integrate physical, social, and biological sciences, and scale from the genomic to the biosphere. As Levin notes, societies are complex adaptive systems, composed of individual agents who have their own priorities, and who value the macroscopic features of their societies differently. Resolving those competing perspectives is at the core of addressing sustainability. Under this theme, we will develop research themes and related questions that focus on integrating advances in the theory and mathematical modeling of complex adaptive systems (CAS) with rich empirical work on the actual dynamics of coupled HES and to explore the relevance of new tools in CAS research for addressing their interactions.

**Theme 3: Measuring and Monitoring Progress toward Sustainability**

Development of a science of measuring and monitoring for sustainability is essential for guiding policies and evaluating progress towards improved human well-being and sustenance of the earth's life support systems. Under this theme, we will seek to identify the major priority areas (research themes) in the mathematical sciences for development of a science of sustainability monitoring and measuring that builds on but goes beyond contemporary approaches. As part of this theme, we will seek to provide a conceptual and methodological framework for sustainability measuring and monitoring that confronts inherent issues of scale, aggregation problems and the need to develop common metrics for sustainability. Specifically, we will seek to answer the questions: What are the critical mathematical sciences research developments necessary for sustainability monitoring and measuring? Why are these important? And, are they feasible?

**Theme 4: Managing Human-Environment Systems for Sustainability**

The planet faces enormous sustainability challenges. With a still-growing human population and rapidly increasing consumption, society must determine how to meet the basic needs of people for food, energy, water, and shelter without degrading the planet's life support infrastructure, its atmosphere and water resources, the climate system, and species and ecosystems on land and in the oceans on which we and future generations will rely. For example, given current trajectories, it has been predicted that society will have to double food production in the next 40 years to keep pace with demand, while reducing pollution impacts on aquatic ecosystems and reducing the rates of biodiversity loss associated with land-use change and overfishing. An improvement in well-being within this ambitious scenario would require improved livelihood opportunities for the poor and a shift in human behavior among others toward goals that seek well-being through a less consumptive lifestyle. This would necessitate radical changes in the management of human-environment systems for sustainability. Under this theme, we will explore potential strategies for managing complex adaptive systems with real actors, polycentric problems, and multiple scales of interactions, starting with the need for precise mathematical formulations of these challenges. This requires going beyond identifying the mathematical challenges to sustainability management of human systems (e.g., population, consumption, environmental externalities, and commons problems) to developing a fundamental, mathematically-based understanding of exactly what management means, what information is required to do good managing, and how one measures the performance of management systems that aim at sustainability. Moreover, it requires developing an understanding of how shifts in human behavior can be achieved in a more effective way. For example, such shifts may arise more readily if risks associated with various responses can be defined in an appropriate probabilistic framework and presented so as to most effectively provide general public appreciation of the trade-offs involved in various management actions.

In addition to these four themes, we anticipate that two areas of emphasis will contribute toward organization of the meeting: **mathematical areas of emphasis** (like large data sets, statistical methods, dynamic models, computational methods) and scientific/societal areas of emphasis (like climate change, energy efficiency, food supply, clean water for drinking and agriculture, diverse and sustainable natural environments, healthy economic systems). As result of interplay before the workshop, a fifth focus group, on Energy, has been created. A key facet of the workshop will be its focus on the mathematical areas of emphasis and their interplay with the **scientific/societal** areas of emphasis.

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Document last modified on November 23, 2010.