Carlos Simpson

Abstract: Over a Riemann surface, given a spectral curve for the group SL(3) we can look for harmonic maps to buildings whose differential is given by the associated triple of 1-forms. Gaiotto-Moore-Neitzke have introduced the spectral network associated to the spectral curve. We describe a combinatorial process, starting from the differentials, to construct the image of the harmonic map. A pre-theorem is that if the spectral network has no BPS states then the reduction process is well-defined, and we conjecture that it terminates. This will give information on WKB asymptotics. The reduction process may be viewed as a 2-dimensional generalization of the Stallings core graph construction. This is joint with Katzarkov, Noll and Pandit.