Recorded 08 May 2024. Yuval Peled of the Einstein Institute of Mathematics presents "Sharp Threshold for Rigidity of Random Graphs" at IPAM's Statistical Mechanics Beyond 2D Workshop. Abstract: Suppose that n vertices are placed generically in R^d, and consider the Erdos-Rényi evolution of random graphs, where a new uniformly distributed edge is added to the graph in every step. We discover the moments in the evolution in which the graph becomes (with high probability) 1. Rigid: the only way to continuously move the vertices while preserving all the distances between adjacent vertices is induced by an isometric motion of R^d. 2. Globally rigid: the embedding of the vertices can be reconstructed, up to isometry, from the distances between adjacent vertices. Joint work with Alan Lew, Eran Nevo, Orit Raz. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-mechanics-beyond-2d/