Mircea Mustaţă
University of Michigan, Ann Arbor, United States

I will discuss a certain invariant of singularities, the minimal exponent, defined for hypersurface singularities and recently extended to complete intersections. I will explain how this invariant governs two classes of singularities that have been introduced recently, the $k$-Du Bois and $k$-rational singularities, refining the classical notions of Du Bois and rational singularities.