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Seminar

Fellowship of the Ring, National Seminar: Commutative Algebra with S_n-invariant monomial ideals May 21, 2020 (01:30 PM PDT - 03:30 PM PDT)
Parent Program: --
Location: MSRI: Online/Virtual
Speaker(s) Claudiu Raicu (University of Notre Dame)
Description

To attend this seminar, you must register in advance, by clicking HERE.

Consider a polynomial ring in n variables, together with the action of the symmetric group by coordinate permutations. In my talk I will describe many familiar notions in Commutative Algebra in the context of monomial ideals that are preserved by the action of the symmetric group. These include Castelnuovo-Mumford regularity, projective dimension, saturation, symbolic powers, or the Cohen-Macaulay property. My goal is to explain how changing focus from minimal resolutions to Ext modules can lead to a simplified picture of the homological algebra, and to provide concrete combinatorial recipes to determine the relevant homological invariants.

 

Video

Commutative Algebra With S_n-Invariant Monomial Ideals

Abstract/Media

Consider a polynomial ring in n variables, together with the action of the symmetric group by coordinate permutations. In my talk I will describe many familiar notions in Commutative Algebra in the context of monomial ideals that are preserved by the action of the symmetric group. These include Castelnuovo-Mumford regularity, projective dimension, saturation, symbolic powers, or the Cohen-Macaulay property. My goal is to explain how changing focus from minimal resolutions to Ext modules can lead to a simplified picture of the homological algebra, and to provide concrete combinatorial recipes to determine the relevant homological invariants.

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Commutative Algebra With S_n-Invariant Monomial Ideals

H.264 Video 25030_28418_8358_Commutative_Algebra_with_S_N-Invariant_Monomial_Ideals.mp4