Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Mochizuki, TakuroSabbah, Claude2024-10-182024-10-182023https://oa.tib.eu/renate/handle/123456789/17103https://doi.org/10.34657/16125The purpose of this Arbeitsgemeinschaft is to introduce the notion of twistor $\mathcal{D}$-modules and their main properties. The guiding principle leading this discussion is Simpson's "meta-theorem", which gives a heuristic for generalizing (mixed) Hodge-theoretic results into (mixed) twistor-theoretic results. The strength of the twistor approach is that it enables to enlarge the scope of Hodge theory not only to arbitrary semi-simple perverse sheaves, equivalently semi-simple regular holonomic $\mathcal{D}$-modules via the Riemann-Hilbert correspondence, but also to possibly semi-simple irregular holonomic $\mathcal{D}$-modules. An overarching goal for this session is Mochizuki's proof of the decomposition theorem for semi-simple holonomic $\mathcal{D}$-modules on a smooth complex projective variety, first conjectured by Kashiwara in 1996.eng510ArticleKonferenzschrift