### The infinitesimal rigidity of symmetric bar-joint frameworks

Combinatorics Seminar

23rd April 2024, 11:00 am – 12:00 pm

Fry Building, 2.04

A (plane bar-joint) framework is a realisation of a finite simple graph in the Euclidean plane. The terms 'bar' and 'joint' refer to the realisations of the edges and vertices, respectively. Throughout this talk, I will concentrate on plane frameworks which present a non-trivial symmetry. A framework is said to be infinitesimally flexible if, roughly speaking, you can shake some (or all) of its joints to deform the framework. Otherwise, a framework is called infinitesimally rigid. The aim of my research is to combinatorially characterise infinitesimally rigid symmetric bar-joint frameworks. During this talk, I will introduce the main tools used for such characterisations, and will present some of the results I have obtained.

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