Some shelling orders are better than others

A shelling order is a recursive way of constructing a polyhedral complex that helps to understand several topological, algebraic and combinatorial invariants. Consequently, a significant amount of effort has been put into developing techniques to determine if a given complex has a shelling order. In this talk we will explore a different point of view that is less popular: for a complex that admits many shelling orders, a good choice of the shelling order can can make a significant difference. We address this problem for matroid independence complexes, present an intriguing connection with shelling orders of polytopes, and discuss some experiments aimed at better understanding some old problems. This is based on joint work Alex Heaton.