Johannes Horn will speak on

Resolving rank 2 spectral covers by semi-stable curves

Abstract: Hitchin systems are fibrations over the so-called Hitchin base by Jacobian/Prym varieties associated to a family of generically smooth spectral covers of a fixed smooth projective curve. However, the spectral curves develop singularities over a discriminant locus in the Hitchin base. Given the Deligne-Mumford compactification of the moduli space of curves it is natural to ask for a resolution of the family of spectral curves by (semi-)stable curves and whether the spectral correspondence extends to such setup.
After a gentle introduction to Hitchin systems, I will explain how the space of quadratic multi-scale differentials with simple zeros leads to a satisfactory answer to these questions in the rank 2 case.