Geometry Seminar
Hitchin-Ngô Lab Seminar - A complex hyperKähler extension of the Weil-Petersson metric
Speaker: Andrea Seppi (Università di Torino)Date: Monday, 19 October 2026 - 11:30-12:30Place: Aula Naranja, ICMAT
Abstract:
It is a classical fact, going back to Weil and Ahlfors around 1960, that the Teichmüller space has a natural Kähler structure, called the Weil-Petersson metric. Many interesting extensions have been studied: Donaldson in 2003 constructed a hyperKähler extension on the space of quasi-Fuchsian manifolds, Loustau-Sanders then built a complex bi-Kähler extension, whereas in my work with Mazzoli and Tamburelli we constructed a para-hyperKähler extension on an analogue space of Anti-de Sitter manifolds.
In this talk, I will explain that all these extensions are in fact restrictions of a natural, holomorphic, "complex hyperKähler'' structure defined on a larger space. If time permits, I will describe the crucial role played by minimal immersions in the complex Lie group PSL(2,C).
