## Combinatorics and Probability Seminar

Corrine Yap

Rutgers

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. Some well-studied examples include graphs, abelian groups, and geometric sets. In this talk, we'll consider the reconstruction of random pictures (n-by-n grids with binary entries) and prove a nearly-sharp threshold. Our main proof technique is an interface argument commonly used in percolation theory.

Monday September 13, 2021 at 2:00 PM in 636 SEO