Christos Athanasiadis: Flag subdivisions and local h-vectors

The enumerative theory of subdivisions of simplicial complexes was developed by Stanley in order to understand the effect of simplicial (and more general type of) subdivision on the h-vector of a simplicial complex. A key role in the theory is played by the concept of a local h-vector. This talk will focus on (a) some new developements and applications of this theory to subdivisions of flag simplicial homology spheres and their γ-vectors, and (b) examples of simplicial subdivisons for which the computation of the local h-vector leads to interesting enumerative problems on objects such as words, colored permutations and noncrossing partitions. Several related open problems will also be discussed.