Algebra and Algebraic Geometry Seminar - Adam Van Tuyl - Componentwise linear ideals and the Herzog-Hibi-Ohsugi Conjecture
Speaker: Adam Van Tuyl
Title: Componentwise linear ideals and the Herzog-Hibi-Ohsugi Conjecture
Abstract: Componentwise linear ideals were introduced by Herzog and Hibi in 1999. In this talk, I will provide a survey on these ideals, with an emphasis on the case of monomial ideals. In particular, I will describe the relationship between these ideals and sequentially Cohen-Macaulay simplicial complexes. Given a componentwise linear ideal I, it is not entirely clear when a powers of this ideal, that is I^s, also inherit the componentwise linear property. Herzog-Hibi-Ohsugi have conjectured that all powers of the cover ideal of a chordal graph have this property. We also survey progress on this conjecture.
Date: Monday Sept 20th, 12:30-1:30