Speaker: Thiago Holleben (Dallhousie University)

Abstract: Given a simplicial complex D, we may associate to it a sequence of numbers usually called graded betti numbers, which consists of information on the homology of induced subcomplexes of D. This sequence has been extensively studied, and it is well known that it can be used to compute f and h vectors of simplicial complexes. In 2022, Cooper et al conjectured that when a simplicial complex comes from the power of a StanleyReisner ideal, graded betti sequences can be bounded by the fvector of a specific simplicial complex defined in terms of integer programs. In this talk, we will talk about a special case of this conjecture, and the face structure of these complexes. This is joint work with Trung Chau, Art Duval, Sara Faridi, Susan Morey and Liana Şega.

The Graduate Online Combinatorics Colloquium is an online combinatorics seminar organized for and run by graduate students.