at the
American Institute of Mathematics, Palo Alto, California
organized by
Troy Day, Zhilan Feng, and Priscilla Greenwood
This workshop, sponsored by AIM and the NSF, has the objective of generating new ideas about how to model spatial problems arising in epidemiology, ecology, evolution, and other areas involving population dynamics. There will be people who are expert in stochastic modeling, others in deterministic modeling, and a few people already combining these approaches. Some specific techniques that will be examined include patch models, or metapopulations, interacting particle systems and their diffusion limits, graphical models, agent based models, branching diffusions, "small world" models.
Some typical problems which require explicitly spatial modeling are: How fast and in what patterns does an epidemic spread? How does the spatial form of local communities effect the coexistence of species which may be competing for resources, or involved in other kinds of ecological interactions?
An hypothesis that underlies much spatial modeling is that individuals interact only with their neighbors, or occasionally over a distance, but not uniformly with all other individuals. This hypothesis allows us to model evolution of interacting populations living in spatially explicit habitats or moving. In several examples, critical values are raised above their values for analogous uniformly mixed populations. Whereas stochasticity may not change critical values, focus on probability distributions broadens our decision space to include the variety of possible behaviors of a population system and the likelihoods associated with these possibilities.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
For more information email workshops@aimath.org
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