If you experience any technical difficulties with this video or would like to make an accessibility-related request, please send a message to [email protected]. This is the first in a series of lectures in the seminar “Combinatorics and Theoretical Computer Science: The Local Certificates Algorithm” at the University of Chicago, given by László Babai, the George and Elizabeth Yovovich Professor in the Departments of Computer Science and Mathematics at the University of Chicago. The lecture took place on November 10, 2015.