Graph rigidity in normed spaces (or: How I learned to stop worrying and love the norm)

Sean Dewar, The Fields Institute and RICAM

Workshop on Progress and Open Problems in Rigidity Theory

Date and Time: Monday, February 22, 2021 - 1:30pm to 2:30pm

Abstract: When handling problems that involve graph is rigidity in a Euclidean space, we can draw from a wealth of literature and our own understanding of how structures behave in everyday life. Things are strikingly different when we switch to a non-Euclidean norm; what was once an obvious fact will not always be so trivial, and it can sometimes feel like up is down and black is white. Occasionally, however, certain rigidity properties can simplify beautifully in a way that we could never hope for in Euclidean spaces. For example, it is conjectured that for non-Euclidean smooth lp spaces, the appropriate Maxwell counting condition (with a sparsity assumption preventing overly-dense subgraphs) is not only necessary but sufficient for rigidity. In my talk I shall present a general survey of graph rigidity in normed spaces, and also outline some recent results and interesting open problems in the area.