Title: Buchsbaum theories for Frobenius and tight closure

Abstract: This talk is on upcoming joint work with Kriti Goel, Lance E. Miller, and Austyn Simpson. For local rings of points on an algebraic variety, the Buchsbaum condition is a well-studied property which assures that a certain measurement of singularity is constant along all parameter ideals. Recently, L. Ma and P.H. Quy introduced the tight Buchsbaum condition, which incorporates the celebrated tight closure of Hochster and Huneke to categorize singularity. In this talk, we will discuss additional variants of the Buchsbaum condition which incorporate Frobenius closure as well.