Aarhus University Seal / Aarhus Universitets segl

QGM seminar by Nikita Nikolaev (Univ. Geneva)

Title: Abelianisation of Logarithmic sl(2)-Connections

2019.02.20 | Jane Jamshidi

Date Wed 27 Feb
Time 13:05 14:05
Location 1531-113 (Aud.D1)

Abstract: 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.