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Uwe Nagel: Stabilization in Sequences of Symmetric Ideals

Time: Mon 2021-11-15 15.00 - 16.00

Location: Zoom, meeting ID: 624 7227 8933

Lecturer: Uwe Nagel (University of Kentucky)

Abstract

Families of ideals arising in various contexts often have a rich algebraic structure, reflected, for example, in a large symmetry group. It is natural to expect that the properties of related ideals remain somewhat invariant even when the ideals involve more and more variables. Indeed, recently a framework has been developed for providing rigorous justifications for this expectation. It led to establishing asymptotic results for invariants such as the Hilbert function and multiplicity as well as graded Betti numbers and Castelnuovo–Mumford regularity. However, the boundaries for this type of results are not clear, and there are many open questions.