Nathaniel Sagman, University of Toronto
Complex harmonic maps and the Atiyah-Bott-Goldman symplectic form
The field of higher Teichmuller theory has developed alongside the theories of Higgs bundles and harmonic maps to symmetric spaces of non-compact type. In this talk, I aim to give an introduction to harmonic maps and Hitchin components for SL(n,R) (examples of so-called higher Teichmuller spaces), and to present a new development: complex harmonic maps to holomorphic Riemannian symmetric spaces. Along with surveying the basic theory, old and new, I will explain how we used complex harmonic maps to prove that the Atiyah-Bott-Goldman symplectic form determines a pseudo-Kahler structure on the Hitchin component for SL(3,R). This is joint work with Christian El Emam.
MC 5417