P-Smallness of Increasing Families

Explore a 58-minute lecture on the concept of p-smallness in increasing families of subsets, presented by Jinyoung Park from the Courant Institute at NYU. Delve into the intricacies of p-biased product measures, thresholds in random discrete structures, and Talagrand's notion of p-smallness as a certificate for small measures. Examine various problems related to p-smallness of increasing families, drawing from joint research with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham. Gain insights into structural results and the historical significance of thresholds in increasing families, a central focus in the study of random discrete structures.