Wild character varieties are spaces of monodromy data for irregular connections on a curve. On $\BP^1$, the purity conjecture of Hausel-Rodriguez-Villegas identifies the pure part of their cohomology with the cohomology of the so-called open de Rham space through the Riemann-Hilbert map. In this talk I will provide evidence for this conjecture by computing the motivic classes of open de Rham spaces using a Fourier transform on Grothendieck rings. This is joint work with Tamas Hausel and Michael Wong.

Bio:

Dimitri Wyss is a Swiss mathematician. Wyss earned his doctorate from EPF Lausanne/ IST Austria in 2017 under the supervision of Tamas Hausel. He is currently a postdoctoral fellow in Sorbonne Université, Paris 6, with François Loeser. His research uses ideas from $p$-adic and motivic integration to study the geometry and topology of moduli spaces arising in non-abelian Hodge theory.