James Cruickshank

Simplicial Complexes and Rigidity

Abstract Simplicial Complexes are fundamental objects of interest in combinatorics, that also arise naturally in geometry, topology and algebra. On the other hand rigidity theory is a subdiscipline of discrete geometry that explores combinatorial and geometric aspects of structures that have some associated notion of flexibility/rigidity. The prototypical example of such a structure is a bar-joint framework, but many variations and generalisations have been explored in the literature. Classically, rigidity theory was most often studied in connection with objects that could be combinatorially modelled by a graph. However, in recent years there have been many interesting developments relating combinatorial aspects of simplicial complexes to the rigidity theory of graphs and hypergraphs. In this talk I will survey some of these developments, with a focus on recent joint work from a series of papers with Bill Jackson and Shin-ichi Tanigawa. I will not assume that audience is familiar with rigidity theory.