Rigidity of 3-Colorings of the d-Dimensional Discrete Torus

Computer Science/Discrete Mathematics Seminar II
Topic:Rigidity of 3-Colorings of the d-Dimensional Discrete Torus
Speaker:Ohad Feldheim
Affiliation:Tel Aviv University
Date:Tuesday, October 18
Time/Room:10:30am - 12:30pm/S-101
Video Link:https://video.ias.edu/csdm/d-dimen

We prove that a uniformly chosen proper coloring of Z_{2n}^d with 3 colors has a very rigid structure when the dimension d is sufficiently high. The coloring takes one color on almost all of either the even or the odd sub-lattice. In particular, one color appears on nearly half of the lattice sites. This model is the zero temperature case of the 3-states anti-ferromagnetic Potts model, which has been studied extensively in statistical mechanics. The proof involves results about graph homomorphisms and various combinatorial methods, and follows a topological intuition. (Joint work with Ron Peled.)