Abstract:

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Singularities are measured in different ways in characteristic zero, positive characteristic, and mixed characteristic. However, the classes of singularities usually form analogous groups with similar properties, with an example of such a group being klt, strongly F-regular and BCM-regular.  In this talk we shall focus on a mixed characteristic counterpart of F-injective and Du Bois singularities.  We will see that the three have a unified description and satisfy many expected properties.