k-Du Bois and k-rational singularities are recently introduced refinements of the classical notions of Du Bois and rational singularities, and they have been extensively studied in the local complete intersection (lci) case. Building on a well known result of Kovács that rational singularities are Du Bois, we prove that k-rational singularities are k-Du Bois. This extends previous work of Mustaţă-Popa and Friedman-Laza in the lci and the isolated singularities cases. Additionally, since Kähler differentials are typically not reflexive outside the lci case, we propose new definitions of these singularities that depend only on the cohomologies of the Du Bois complex and not on the behaviour of Kähler differentials. This is based on joint work with Wanchun Shen and Anh Duc Vo.

Zoom ID:  https://arizona.zoom.us/j/83621467612