Frontiers of Mathematics in Geosciences

Mathematics is a fundamental tool of the geosciences, with many branches of the geosciences using sophisticated mathematics to address research problems. However, there is an increased need for communication among geoscientists and mathematicians to encourage the development of mathematical frontiers for geoscience research, to understand how mathematical methods can be applied across disciplinary boundaries in the geosciences, and to identify areas of the geosciences that could benefit from new developments in mathematics.

The aim of this workshop is to bring together scientists from the broad spectrum of disciplines within both geoscience and mathematics who are interested in a mathematical approach to geoscience problems.

The workshop has two goals:

(1) To identify geoscience research topics that would benefit from a sophisticated mathematical approach, or are likely to stimulate new mathematics research.

(2) To foster interdisciplinary communication among researchers who may potentially collaborate on mathematical and geoscience research topics and, in particular, to promote contacts between geoscientists and mathematicians.

The workshop will be structured so as to encourage cross-disciplinary communication, with many opportunities for discussion among participants.  We hope that one of the outcomes of the workshop will be to stimulate new research collaborations both in mathematics and in geosciences. One of NSF's hopes is that this program will provide an assessment of research opportunities that NSF can use for future programs.

The capacity of this workshop is limited.

The conference, a brainstorming meeting, will be organized around alternating plenary sessions and smaller breakout groups, with few talks. Among the topics to be discussed are:

- Theory, simulation, and visualization of systems with very large numbers of interacting components;

- Quantifying uncertainty in complex systems;

- Langrangian transport in geofluids;

- The dynamics of the geodynamo;

- Links between geostrophic and inertial turbulence;

- Mixing and stirring in geofluid systems;

- Analysis of sparse and intermittent data (and intermittency itself);

- The evolution of complex hydrological structure;

- Mathematical approaches to biogeochemical systems