Seminar Announcement
Speaker: Ngo Viet Trung, Institute of Mathematics, Hanoi, Vietnam
Date: Tuesday, 19 December 2023
Time: 3.30 - 4.30 PM
Venue: Lecture Hall 01
Depth functions of homogeneous ideals
Ngo Viet Trung
Institute of Mathematics, Hanoi, Vietnam.
19-12-23

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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 on 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.