Dynamics on Wild Character Varieties

[摘要] In the present paper, we will first present briefly a general research program about the study of the ''natural dynamics'' on character varieties and wild character varieties. Afterwards, we will illustrate this program in the context of the Painlevé differential equations $P_{\rm VI}$ and $P_{\rm V}$.

[关键词] character varieties;wild fundamental groupoid;Painlev´e equations