Title: Euclidean and projective rigidity of hypergraphs
| Speaker: |
Signe Lundqvist |
| Affiliation: |
Umeå University |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: The mathematical theory of structural rigidity has a long history. In the nineteenth century, Cauchy studied rigidity of polyhedra, and Maxwell studied graph frameworks. The rigidity theory of graph frameworks has since been studied extensively. Pollaczek-Geiringer, and later Laman, proved a combinatorial characterization of the minimally rigid graphs in the plane.
Combinatorial rigidity theory is also concerned with geometric realizations of other combinatorial structures. In this talk, we will focus on rigidity of realizations of hypergraphs as points and straight lines. We will discuss how to determine whether a realization of a hypergraph is rigid, in the sense that there are no motions of the realization that preserve the incidences of points and lines, and the distance between any pair of points that lie on a line.
We will also discuss motions of realizations of hypergraphs that preserve only the incidences between points and lines. We will see that classical theorems in incidence geometry, such as Pascal's theorem, make determining rigidity with respect to such motions a difficult problem.
The talk will be based on joint work with K.Stokes and L-D. Öhman, as well as work in progress, joint with L.Berman, B.Schulze, B.Servatius, H.Servatius, K.Stokes and W.Whiteley.