Michael Groechenig (Toronto)

Hypertoric Hitchin systems and p-adic integration

A construction due to Hausel and Proudfoot associates to a graph a complex-analytic integrable system. In this talk I will describe a formal-algebraic analogue of their construction, and explain how one can compute the p-adic volumes of the generic Hitchin fibres in graph-theoretic terms. This is joint work with Michael McBreen.