# Schubert Varieties, Equivariant Cohomology and Characteristic Classes

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#### DOI: 10.4171/182-1/8

Characteristic classes of mixed Hodge modules and applications

Laurentiu Maxim[1] and Jörg Schürmann[2]

(1) University of Wisconsin, Madison, USA
(2) Universität Münster, Germany

We give an overview, with an emphasis on applications, of recent developments on the interaction between characteristic class theories for singular spaces and Saito's theory of mixed Hodge modules in the complex algebraic context.

Keywords: Characteristic classes, Atiyah–Singer classes, mixed Hodge modules, $V$-filtration, nearby and vanishing cycles, singularities, toric varieties, hypersurface, symmetric product, generating series.