Speaker: Byron Chin (MIT)

Title: Exact threshold for non-linear Hamilton cycles

Abstract:

In this talk, I will discuss some recent work determining the threshold for the appearance of Hamilton cycles -- that is a cycle using all of the vertices -- in random hypergraphs. The result confirms behavior conjectured by Narayanan and Schacht. The main difficulty comes from the fact that the usual second moment method does not suffice. I will talk about a technique to improve the second moment method, known as small subgraph conditioning, and how it applies to this setting.