DMS Combinatorics Seminar

Speaker: Corrine Yap (Georgia Tech)

Title: Reconstructing Random Pictures

Abstract: Reconstruction problems ask whether or not it is possible to uniquely build a discrete structure from the collection of its substructures of a fixed size. This question has been explored in a wide range of settings, most famously with graphs and the resulting Graph Reconstruction Conjecture due to Kelly and Ulam, but also including geometric sets, jigsaws, and abelian groups. In this talk, we'll consider the reconstruction of random pictures (n-by-n grids with binary entries) from the collection of its k-by-k subgrids and prove two-point concentration for the threshold value of k = k(n). Our main proof technique is an adaptation of the Peierls contour method from statistical physics. Joint work with Bhargav Narayanan.