Recent progresses in the unanimity problem in Majority Dynamics on random graphs

Majority Dynamics is a process on a graph, where each vertex starts out with a Red or Blue color, then on each day changes its color to the majority color among its neighbors the previous day. If at some point one color covers every vertex, that color is said to win and such state is called unanimity. Research on unanimity has traditionally focused on the model where initial colors are independently chosen with 1/2 chance, and the graph is generated on them from the G(n, p) model. In this talk, we discuss how recent studies by many authors point out that, fixing the initial colors instead can help answer some of the questions in the traditional model, and pose new interesting conjectures.