Wednesday Discussion on Geometric Issues

This session was moderated by John Shareshian. The discussion started off with some comments about Riemannian metrics and whether the set of metrics on tree space would be useful to study.

Q. Are there many useful or interesting metrics on tree space?

Q. Is the BHV metric the only one (up to scalars) of non-positive curvature? (Bridson)

Q. What metrics ``should'' be used on the subspace obtained by fixing the tree type?

Q. How does the Robinson-Foulds metric compare with the BHV metric? (Diaconis) What's the Lipshitz constant? (Bridson)

Q. Should the metric on tree space come from an intrinsic metric, or an extrinsic metric on a larger space in which tree space is embedded? Which is a more natural way to view tree space?

Q. How do you deliver geometry to biologists? (Billera)

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