Laurenţiu Maxim
University of Wisconsin-Madison, USA

The notions of higher Du Bois and higher rational singularities of hypersurfaces were recently introduced and studied by Jung-Kim-Saito-Yoon, Mustata-Olano-Popa-Witaszek and Friedman-Laza, as natural generalizations of Du Bois and rational singularities, respectively. In this talk I will present a homological characterization of these notions, in terms of characteristic classes introduced in prior work with M. Saito and J. Schuermann. As a preliminary step, I will describe such singularities using the Hodge filtration on the vanishing cycle complex. (Joint work with R. Yang and M. Saito.)