## Algebra and Algebraic Geometry Seminar - Adam Van Tuyl - Componentwise linear ideals and the Herzog-Hibi-Ohsugi Conjecture

- Calendar
- Mathematics & Statistics

- Date
- 09.20.2021 12:30 pm - 1:30 pm

### Description

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

Location: Virtual

Zoom Link: https://mcmaster.zoom.us/j/96350226417?pwd=UkpXbXVZVnFnb2puOVpCVFlJSk1RZz09