Rigidity of 2D and 3D quasicrystal frameworks

Abstract: Deciding wether a generic 2D rod-and-pinion framework is rigid can be done by checking that its underlying graph satisfies the Laman conditions. For frameworks with a special configuration such as grids of squares, there is a simpler way to associate a graph to the framework and decide if it is rigid or not. In this talk I will consider frameworks that come from Penrose tilings and show that we can decide the rigidity of these frameworks as we do for grids of squares. There is no generalization of Laman conditions for rigidity of 3D graphs but perhaps we can prove (conjecture) a generalization of 2D results for cubical frameworks or 3D quasicrystals. Pictures and real time interactive animations will be present throughout this talk to illustrate important concepts. This talk is based on joint work with George Francis and students from the Illinois Geometry Lab.

combinatorics

Audience: researchers in the topic

( slides | video )

Virtual seminar on algebraic matroids and rigidity theory

Series comments: The COVID-19 pandemic is forcing us all to stay home, foregoing conferences and departmental seminars for the next few months. This weekly virtual seminar is an attempt to patch that departmental-seminar-sized void in our lives until it is safe to resume our more traditional forms of professional networking. Since geographic location matters a lot less for a virtual seminar than for an in-person seminar, this virtual seminar will be defined purely by its mathematical theme, algebraic matroids and rigidity theory, and not any particular department nor region.