Combinatorial Methods in Topology

This research program contains three projects in combinatorial topology.

The problems that are addressed in this research investigate whether higher dimensional analogues for some significant graph theoretic results exist.

Moreover, they are mainly concerned with a study of topological properties of spaces through combinatorial data from their triangulations.

These problems are motivated by the study of two major open problems in this area; namely the g-conjecture and the Charney-Davis conjecture.

The primary aim of this research is to develop and better understand the geometric and topological ideas around this circle of problems.

The long-range goal is to make contribution to this area and hopefully contributing to the solutions of these two major open problems.