MSI Weekly Bulletin - Week starting Monday 13 March, 2006

In the past 20 years, various problems in geometry have been shown to be "integrable systems", which roughly means that families of solutions are obtained by maps into certain loop groups. One of the interesting recent techniques for producing solutions is the DPW (Dorfmeister/Pedit/Wu) method, < used the Birkhoff factorization Theorem to simplify the problem of producing harmonic maps into symmetric spaces. I will discuss the generalizatin of this method, and an application: specifically, that the (local) problem of producing constant curvature submanifolds of a sphere or hyperbolic space can be reduced to the case where the submanifold is flat.

A PDF file of the paper is available at http://www.nature.com/nrg/journal/v5/n8/full/nrg1402_fs.html If time permits, we will also look at: "Maintenance of ancestral complexity and non-metazoan genes in two basal cnidarians", by Ulrich Technau et al., Trends in Genetics 21 (2005) 633--639