Rigidity theory considers ensembles of balls connected by rigid rods 
which constrain the displacements of the balls.
Depending on the number of rods, the system may be floppy or rigid, and 
the two phases are separated by a percolation-like
transition. Beyond mechanical systems, this idea has been used for 
instance to model network forming glasses and proteins.
In this talk, we will first present the basis of rigidity theory and 
some open problems in the field.
We will then show how the study of some exactly solvable models may shed 
light on these problems.
We will in particular be interested in models on random graphs, which 
will be dealt with using the so-called "cavity method",
and models on hierarchical graphs, for which we will use a 
renormalization approach.

Collaborators: Avadh Saxena, Turab Lookman, Alan Bishop (Los Alamos, USA);
	       Olivier Rivoire (Rockefeller University, USA)