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University of Sydney Algebra Seminar

Thomas Le Fils

Friday 11 November, 12-1pm, Place: Carslaw 173

Holonomy of complex projective structures and periods of abelian differentials

I will introduce complex projective structures surfaces i.e. geometric structures modeled on the Riemann sphere with Mobius transformations as transition maps. Such a structure gives rise to a homomorphism of the fundamental group of the surface into PSL(2, C): its holonomy. I will address the question of characterizing the homomorphisms that arise as the holonomy of a projective structure with branch points on a surface. I will give particular attention to the case of translation surfaces: projective structures obtained by gluing sides of polygons with translations. This will lead us to the characterisation of the periods of abelian differentials on complex curves.