This is perhaps one of the most important issues that our community faces. A broad coverage should facilitate freshness and innovation along with continuity. It should allow for novel problems and applications, and recognize new ideas or techniques originating in other parts of mathematics and computer science that address old open questions.
The community must be open and recognize both the results emerging from larger-scale, well-funded research projects, as well as those coming from individual, perhaps more isolated researchers. A broad coverage may be stiffled by the effect of establishment, connections, name recognition or coasting on reputation. A broad coverage should allow co-existence of fundamental results with hot, application-oriented ones. A broad coverage should invite participation in our conferences of
members of other communities whose problems and techniques are geometrical.
What should we do to facilitate/ensure a broad coverage of topics?