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Abelianisation of Logarithmic sl(2)-Connections

Nikita Nikolaev (University of Geneva)
Wednesday 27 February 2019 13:00–14:00 Aud. D1 (1531-113)
I will describe an approach, called abelianisation, to studying logarithmic connections on vector bundles of higher rank over a complex curve X by putting them in correspondence with logarithmic connections on line bundles (a.k.a. abelian connections) over a multi-sheeted cover p: S -> X. In this talk, I will explain an equivalence between a category of logarithmic sl(2)-connections on X with fixed generic residues and a category of abelian logarithmic connections on an appropriate double cover p: S -> X. The proof is by constructing a pair of inverse functors, and the key is the construction of a certain canonical cocycle (which I call the Voros cocycle) valued in the automorphisms of the direct image functor p_*. Based on arXiv:1902.03384.
Organised by: QGM
Contact: Sergey Arkhipov Revised: 20.02.2019