Ben Moonen: The Coleman-Oort problem - an update

Abstract:

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.