Nevo

Eran Nevo

"Around the g-conjecture"

A major open problem in algebraic combinatorics is McMullen's 1970 g-conjecture, which suggests a characterization of the face-vectors of simplicial spheres. The simplicial polytopes case was proved by Billera-Lee (sufficiency) and Stanley (necessity) in 1980, known as the g-theorem.

I will discuss some results and problems brunching from this conjecture, from old to very recent: for more general objects (e.g. triangulated manifolds, doubly Cohen-Macaulay complexes), special cases (e.g. PL-spheres, flag spheres), and related objects (e.g. cubical polytopes, complexes embedded in spheres). In particular, an analog of graph rigidity theory, for bipartite graphs, will be considered. The latter is joint work with Gil Kalai and Isabella Novik.