The Deligne-Hitchin moduli space is a partial compactification of the moduli space of $\lambda$-connections. It includes as closed subvarieties the moduli spaces of Hitchin bundles ($\lambda=0$) and of holomorphic connections ($\lambda=1$), exhibiting the later as a deformation of the former. We show a Torelli theorem for a parabolic version of this moduli space (joint work with David Alfaya). I will try to make the talk accessible to a wide mathematical audience.

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Last updated: 09 Apr 2019