Abstract:
Groechenig, Wyss and Ziegler have recently proved a conjecture of Hausel and Thaddeus concerning an equality between stringy Hodge numbers of moduli spaces of Higgs bundles for $\mathrm{SL}_n$ and $\mathrm{PGL}_n$. A crucial ingredient in their approach is the use of $p$-adic integration in the fibres of the Hitchin fibration. I will start by presenting some old work with Jan Denef on the McKay correspondence (on resolutions of quotients by finite groups) that reappears in this context and then discuss a motivic version of the results of Groechenig, Wyss and Ziegler which is joint work with Dimitri Wyss.