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Ben Moonen: The Coleman-Oort problem - an update


Tid: To 2024-05-23 kl 15.40 - 16.40

Plats: Classroom 7, Albano House 1, Floor 2

Medverkande: Ben Moonen (Nijmegen)

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A conjecture of Coleman says that if we fix a genus \(g\) (with \(g>7\)), there are only finitely many complex curves (smooth projective, taken up to isomorphism) of genus \(g\) for which the Jacobian is an abelian variety of CM type. Via the André-Oort conjecture (now a theorem of Tsimmerman, building upon work of many others), Coleman's conjecture can be reformulated as a problem about the non-existence of special subvarieties in the Torelli locus. In my talk, I will review this problem, and I will discuss recent progress, based on ideas that come from various directions.