Events
DMS Algebra Seminar |
| Time: Dec 14, 2021 (12:30 PM) |
| Location: 358 Parker Hall |
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Details: PLEASE NOTE CHANGE IN TIME
 Speaker: Hai Long Dao (University of Kansas).
Title: Linearity of Free Resolutions of Monomial Ideals
Abstract: We study \(N_{d,p}\) monomial ideals, namely ones that are generated in degree \(d\) and whose minimal resolution is linear in \(p-1\) steps. We give combinatorial characterizations when \(d=3\) or when the ideal is primary and \(p\) is one less than the number of variables (the almost linear resolution case). We give bounds on regularity, number of generators, and the size of subsets of variables needed to test whether an ideal is \(N_{d,p}\). We construct examples of such ideals with relatively few generators using Sierpi\'nski sieves and higher analogues. Our results also lead to classes of highly connected simplicial complexes \(\Delta\) that can not be extended to the complete \(\dim \Delta\)-skeleton of the simplex on the same variables by shelling.
Joint work with David Eisenbud.
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