Lars Halvard Halle: Lattices of differential forms for degenerations of curves.

I will talk about two numerical invariants associated to a degenerating family of curves; Chai's base change conductor and Edixhoven's jumps. In a joint work with D. Eriksson and J. Nicaise, we show that these invariants can be computed from certain lattices of (logarithmic) differential forms associated to the degeneration. Using log geometry, we obtain conceptual proofs of many of the properties of Edixhoven's jumps (in particular rationality), and we moreover find an explicit combinatorial formula for them.