Calculating harmonic maps to buildings---a 2-dimensional combinatorial reduction calculus


Carlos Simpson

Universite de Nice

Harvard University

Thursday, November 17, 2016


Talk at 4:30 p.m. in Science Center C

Tea at 4:00 p.m. in the Math Lounge


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.


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Posted: November 14, 2016    URL: