Geometric models of biological phenomena

June 1 to 5, 2003

at the

American Institute of Mathematics, Palo Alto, California

organized by

Louis Billera, Susan Holmes and Karen Vogtmann

This workshop, sponsored by AIM and the NSF, will be devoted to the study of how the geometry of "tree space," the space of all rooted trees, can be applied to the solution of problems in biology. A particular focus will be understanding evolutionary relationships, such as reconstructing phylogenetic trees from DNA data. Factors such as conflicts in the original DNA data lead to uncertainty as to the ``true" evolutionary tree; thus a major issue is how to build the tree which best reflects the available data. One possible approach is to cast the problem in terms of finding the center of a collection of points in tree space.

This workshop will bring together researchers in combinatorics, topology, statistics, and biology. We hope especially to facilitate communication between the four groups so that biologists can become aware of the mathematical tools which are available, mathematicians can become aware of the problems which are of interest to biologists, and all four groups can profit from a better understanding of the relationship between statistical and geometric methods.

Some specific questions to be addressed are:

What sorts of biological problems can be modeled in tree space?
The geometry of tree space admits several notions of "center." Which of these is the most significant for biological systems?
What are the important biological questions that can be attacked by geometric and statistical methods, and what new mathematical techniques will be needed?

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. The questions should be 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 there will be ample time between talks for discussions and for work to be done.

Participants include D. Aldous, N. Amenta, E. Babson, Y. Baryshnikov, L. Billera, M. Bridson, R. Charney, P. Diaconis, J. Endler, D. Epstein, S. Evans, D. Flath, R. Forman, N. Glenn, D. Hillis, S. Holmes, J. Huelsenbeck, D. Kozlov, J. Luecke, E. Mossel, D. Penny, D. Pollock, L. Popovic, E. Purdom, J. Shareshian, B. Snel, K. St.John, A. Staple, F. Su, J. Vert, K. Vogtmann, and M. Wachs.

The deadline to apply for support to participate in this workshop has passed.

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