DMS Algebra Seminar

Speaker: Michael Perlman (University of Alabama)

Title: Higher singularities for determinantal ideals

Abstract: Higher Du Bois and higher rational singularities are newly-defined properties of complete intersections that can be detected using local cohomology, refining the classical notions of Du Bois and rational singularities. We will discuss the commutative algebra behind these properties, and a number of challenges that arise while attempting to generalize them outside the complete intersection case. Via the example of determinantal ideals, we will describe multiple possible generalizations.