Combinatorial and geometric rigidity
This course will cover the breadth of combinatorial and geometric rigidity. Concretely we view a framework (G, p) as a realisation of a graph G = (V, E) via a map p assigning positions of Euclidean d-space to the vertices and with respect to which the edges satisfy certain geometric constraints. We will focus on the classical example where the constraints determine edge lengths. We will analyse the rigidity and flexibility properties of such frameworks using tools from graph theory and discrete geometry.
The course will cross-coordinate with the thematic programs' winter school, and other events that will run in parallel during this Fields institute program.
Logistics: This is a semester long graduate course. The course is free and open to all graduate students worldwide. The course should be accessible to any graduate student in mathematics and the only background assumed will be in basic linear algebra, Euclidean geometry and graph theory. Course credit is available through participating institutions.