Large combinatorial objects such as random graphs can exhibit sharp transitions in their structure as they grow. As an example, consider the graph process where we start with a graph with many vertices and no edges and add random edges one by one. There is a rapid change in structure at around the time when the average degree reaches 1. This "Phase Transition"  has been the subject of intense study. In a similar vein we find that many other graph properties, such as connectivity or 3-colorability, appear relatively suddenly at a precise threshold. In this talk we give a brief survey of various aspects of thresholds and phase transitions in combinatorics.

Light refreshments will be served before the lecture at 3:30 p.m.