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Riemann-Hilbert correspondence, irregular singularities and Hodge theory. (English) Zbl 1405.14026
Ji, Lizhen (ed.) et al., Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations. Based on the conference, Institute Mittag-Leffler, Stockholm, Sweden, July 13–18, 2015. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-363-0/pbk). Advanced Lectures in Mathematics (ALM) 42, 315-326 (2018).
Summary: This short text takes up a survey talk on recent results about the Riemann-Hilbert correspondence in case of irregular singularities in higher dimension. It explains the new features of Hodge theory in this wild context, where irregular singularities are present, and exemplifies applications to Landau-Ginzburg potentials.
For the entire collection see [Zbl 1398.14003].
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14D07 Variation of Hodge structures (algebro-geometric aspects)