Geometry Seminar
Complex harmonic maps and Goldman’s symplectic form
Speaker: Nathaniel Sagman (University of Luxembourg)Date: Wednesday, 02 April 2025 - 11:30Place: Aula Naranja, ICMAT
Abstract:
Equivariant harmonic maps play an essential role in many areas of mathematics, including the theory of Higgs bundles and (classical and higher) Teichmuller theory. In this talk, after going over the basics on equivariant harmonic maps and Hitchin components (examples of so-called higher Teichmuller spaces), we will introduce and discuss complex harmonic maps to holomorphic Riemannian symmetric spaces. One motivating factor is that, in some sense, this new theory of complex harmonic maps analytically continues the theory of ordinary harmonic maps, and can be used to study families of representations that vary holomorphically. We will then show how we are using complex harmonic maps to prove that, on every rank 2 Hitchin component, Goldman’s symplectic form is compatible with Labourie’s complex structure, in the sense that they together define a pseudo-Kahler structure. This all joint work with Christian El Emam, some already in print and some in progress.
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The talk will be preceeded by a coffee break at 11h, at the cafeteria of ICMAT.
