Geometry Seminar
Hitchin-Ngô Lab Seminar - 4-cyclic Higgs bundles, ∂-alternating surfaces, and QIE representations
Speaker: Junming Zhang (Nankai University)Date: Thursday, 17 September 2026 - 11:30-12:30Place: Aula Naranja, ICMAT
Abstract:
We introduce ∂-alternating surfaces in complex pseudo-hyperbolic spaces of signature (2,q) or (q+1,1), which generalize maximal surfaces in real pseudo-hyperbolic geometry, and establish a natural correspondence between these surfaces and harmonic 4-cyclic Higgs bundles. Under this correspondence, the Gauss map of the surface agrees with the harmonic map arising from non-Abelian Hodge theory. When the underlying surface is closed, we prove that the associated equivariant harmonic maps are bi-Lipschitz embedded minimal surfaces and that the corresponding surface-group representations into PU(2,q+1) are discrete, faithful, and their orbit maps are quasi-isometric embeddings. We also construct domains of discontinuity in the symmetric space and its Shilov boundary, whose quotients form fiber bundles over the underlying surface. This is joint work with Qiongling Li.
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