Problem of the Week
Hilton Memorial Lecture
The Charney-Davis conjecture is an easily stated linear inequality on the face numbers of simplicial spheres that are also flag complexes, that is, complexes for which every minimal non-face is a two element set. While the conjecture is reasonably well known, it is only known to hold in a handful of rather narrow cases, and the proofs are often very complicated. I will discuss some known results and give an easy proof of a relatively broad case.