Exact threshold for non-linear Hamilton cycles

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.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/