Speaker: Sudipta Das
Date: September 18, 2025
Affiliation: TIFR, Mumbai

Abstract: In this talk, we will discuss the concept of asymptotic colengths for families of $m$-primary ideals within a Noetherian local ring $(R,m)$. We will explore the significance of these colengths in the fields of commutative algebra and algebraic geometry. In any characteristic, we will generalize graded families to weakly graded families of ideals. In prime characteristic, we will investigate various families, including weakly $p$-families. The primary objective of this talk is to present a new analytic method for proving the existence of these limits. If time permits, we will also discuss Brunn-Minkowski type inequalities, positivity results, and volume = multiplicity formulas for these families of ideals. This talk is based on a joint work with Cheng Meng.