Sasha Pevzner:Facets of simplicial complexes with symmetric Stanley–Reisner ideals

Abstract: In recent years, the study of Sym-invariant chains of ideals has garnered significant attention. These are systems of nested ideals of polynomial rings in increasingly many variables which are stable under the action of the symmetric group by variable permutation, and they satisfy an additional compatibility condition. We consider Sym-invariant chains consisting of squarefree monomial ideals. Under the Stanley–Reisner bijection these correspond to sequences of simplicial complexes on increasingly many vertices. Using combinatorial and discrete geometric methods, we provide a description of the facets occurring in these chains of simplicial complexes as well as their growth rates. This is joint work with Ayah Almousa, Kaitlin Bruegge, Martina Juhnke-Kubitzke, and Uwe Nagel.   This talk is given via Zoom, you can also view it in KTH 3721.