Title: Leaping Rigid Chess Pieces
Speaker: Ethan White (UIUC)
Abstract: A framework is an embedding of a graph into Euclidean space. We imagine the vertices have become flexible joints, and the edges have become steel bars. The property we are interested in is rigidity: Can the framework change shape without bending or breaking the steel bars? For example, a triangle is rigid. A square is not, because it can be deformed into a family of rhombi. We resolve a few open questions by constructing 'unexpected' rigid frameworks, namely: frameworks coming from bipartite graphs, and those with large girth as well.
