Room P3.10, Mathematics Building

Bruno A. Simões, FC, Univ. Lisboa
Explicit constructions of harmonic maps into the unitary group

We give a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to the unitary group ${\bf U}(n)$ in any dimension, and so all harmonic maps from the $2$-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual $\overline{\partial}$-problems or loop group factorizations.