Mathematics Colloquium

Wednesday, 13 December, 4 pm

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Venue: Ramanujan Hall

Host: Jugal Verma

Speaker: NV Trung

Affiliation: Vietnam Academy of Sciences, Hanoi

Title: Depth functions of homogeneous ideals

Abstract: Depth is an important invariant of a graded algebra over a field. Let R be a polynomial ring and I a homogeneous ideal. By Auslander-Buchsbaum formula, depth R/I + proj.dim R/I = dim R. In recent years, there has been a surge of interest in the behaviour of the functions depth R/I^t and depth R/I^(t), where I^(t) denotes the t-th symbolic powers of I. It was conjectured that these functions may behave wildly at the beginning. These conjectures have been solved recently. This talk will give a survey on this topic.