Generic symmetry-forced infinitesimal rigidity: translations and rotations

Abstract: Bar and joint frameworks appearing in certain applications (particularly crystallography) are often constrained to have particular symmetries. This motivates the study of symmetric frameworks whose allowable flexes preserve the symmetry. Just as non-symmetric frameworks are represented using graphs, symmetric frameworks are represented using gain graphs, i.e. directed graphs whose arcs are labeled by elements of a group. The main result of this talk is a Laman-like characterization of the gain graphs that are generically infinitesimally symmetry-forced rigid in the plane when the symmetry group consists of translations and rotations.

combinatorics

Audience: researchers in the topic

( paper )

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.