# Eran Nevo: Face enumeration in flag complexes

**Time: **
Wed 2021-03-03 10.15 - 11.15

**Location: **
Zoom meeting ID: 654 5562 3260

**Participating: **
Eran Nevo (Hebrew University)

Abstract: A simplicial complex is called flag if its faces are all cliques of a graph.

Flag complexes pop up in various contexts and have been studied extensively. For example, Turan's theorem upper bounds the number of i-faces given the dimension and number of vertices of the flag complex. Yet, the face numbers of flag complexes are not well understood, particularly when taking into account homological information of the complex. I'll describe some problems and results in this direction:

* regarding (face, Betti)-vectors of flag complexes, based on https://arxiv.org/abs/1908.08308, joint with Ernest Chong, and

** regarding Gal's generalized lower bound conjecture for flag homology spheres, based on https://arxiv.org/abs/1908.08727, joint with Maria Chudnovsky.

All relevant background will be given in the talk.

Zoom link: https://kth-se.zoom.us/j/65455623260

Zoom meeting ID: 654 5562 3260