References

Previous summers

2009

2010

Background

The main background references we'll look at are the following. The links should all work within the Barnard/Columbia network; please e-mail me if you have any trouble.

Local rigidity

Global rigidity

Stresses, SDP, and universal rigidity

Bipartite graph

Affine rigidity

Counting points

Rigidity on torus

Linkages

A linkage is a flexible framework; one nice result is that you can “sign your name” with a linkage.

Other references

Textbooks

Linear algebra

Differential geometry

Graph theory

Graph enumeration

Graph enumeration techniques are clever ways of listing all graphs with a given number of vertices. In the context of rigidity, the key will be to do the search cleverly and prune out partial graphs as quickly as possible. (I haven't yet been

Theory of computation

Geometry

Algebraic Geometry

This is a huge subject, and you should try not to get too bogged down in it&dots; But these references at least have the basic definitions.

Programs

The program from last summer by Frank and Jiang is available here (in .tar.gz format; let me know if you have problems.) Of particular interest even to non-programmers are their detail results, listing all the (many) counterexamples to Hendrickson's conjecture that they found.

Writing

When you get to writing up your results, the following references will be useful: