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On opers and complex lagrangians

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Olivia-Mirela Dumitrescu
Thu, 25/05/2023 - 15:00 - 16:00
MPIM Lecture Hall
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Contact: Christian Kaiser

In 2014 Gaiotto conjectured a correspondence between a holomorphic  lagrangian (Hitchin section) in the Dolbeault moduli space of Higgs bundles on a curve ​and the holomorphic lagrangian of opers in the de Rham moduli space of holomorphic connections. This conjecture was established in 2016 for holomorphic opers with an arbitrary complex simple Lie group; the construction is known today as the conformal limit.

In this talk I will present an algebraic geometry description of conformal limits for SL_n(C).
In rank 2, I will relate this construction with the holomorphic lagrangian foliation conjecture of Simpson. This talk is based on joint work in progress with Motohico Mulase.


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