Wednesday, August 9, 2023

1:00 p.m. (sharp)

Zoom Web Conference

PhD Candidate: Sina Zabanfahm

Co-Supervisors: Michael Groechenig/Lisa Jeffrey

Thesis title: Cluster pictures for Hitchin fibers of rank two Higgs bundles

***

Let φ: X → Y be a degree two Galois cover of smooth curves over a local field F, where F has odd residual characteristic. Assuming that Y has good reduction, we describe a semi-stability criterion for the curve X, using the data of the branch locus of the covering φ. In the case that X has semi-stable reduction, we describe the dual graph of the minimal regular model of X over F. We do this by adopting the notion of the cluster picture defined for hyperelliptic curves for the case where Y is not necessarily a rational curve. Using these results, we describe the variation of the p-adic volume of Hitchin fibers over the semi-stable locus of the moduli space

of rank 2 twisted Higgs bundles.

***

The draft of the thesis can be found here: SZabanfahm-Thesis