Seminar on low-dimensional mathematics Friday, July 4, 2008 Recent results in Combinatorial Rigidity Theory Ileana Streinu, Smith College, USA Rigidity theory starts with Cauchy's celebrated theorem on convex polyhedra, yet not much is known about the rigidity (infinitesimal, generic, combinatorial) of arbitrary structures in three-dimensions. In two dimensions, bar-and-joint rigidity is fully characterized combinatorially by Maxwell-Laman's theorem. How to proceed from here to higher dimensions is an open question. In this talk, I will present a number of my results (some obtained with collaborators and students) on combinatorial rigidity. These include pointed pseudo-triangulations, pebble games and sparsity matroids. --- Home-page of the seminar: http://www.pdmi.ras.ru/~lowdimma