Abstract

Geometric rigidity is a theory that studies geometric structures known as frameworks through tools from various areas of mathematics, including representation theory, algebra, and combinatorics.

One type of framework which is central to rigidity theory is the bar-joint framework, a structure composed of stiff bars linked together by freely rotational joints. The main goal is to determine when such a structure is rigid, i.e. when it cannot be deformed in any way that keeps its bar-lengths fixed.

Under some genericity assumptions, rigidity is well-understood in the Euclidean plane. However, the problem becomes more difficult when we drop the genericity requirements. When introducing symmetry, some frameworks in the Euclidean plane behave in unexpected ways.

In this talk, I will introduce some notions of rigidity and see how symmetry affects rigidity in the Euclidean plane.