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Perversity equals weight for Painlevé systems

Szilárd Szabó
Rényi Alfréd University, Budapest
Tuesday, November 13, 2018 - 11:00

An important conjecture in non-Abelian Hodge theory byde Cataldo, Hausel and Migliorini asserts that the weight filtrationon the cohomology spaces of a character variety agrees with the perverseLeray filtration on the cohomology spaces of the corresponding Dolbeaultmoduli space. We prove an analogous result for wild character varietiesand the corresponding irregular Hitchin systems associated to the Painlevécases. The proof is based on an earlier description of the wild charactervarieties arising in these cases by Marius van der Put and Masa-Hiko Saitoon one hand, and on our study of the geometry of irregular Hitchin systemson the other hand.

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