Thresholds versus fractional expectation-thresholds

ACO Student Seminar
Friday, December 6, 2019 - 1:05pm for 1 hour (actually 50 minutes)
Skiles 005
Jinyoung Park – Rutgers University
Prasad Tetali

Please Note: (This is a joint event of ACO Student Seminar and the Combinatorics Seminar Series)

In this talk we will prove a conjecture of Talagrand, which is a fractional version of the “expectation-threshold” conjecture of Kalai and Kahn. This easily implies various difficult results in probabilistic combinatorics, e.g. thresholds for perfect hypergraph matchings (Johansson-Kahn-Vu) and bounded-degree spanning trees (Montgomery). Our approach builds on recent breakthrough work of Alweiss, Lovett, Wu, and Zhang on the Erdős-Rado “Sunflower Conjecture.” 

This is joint work with Keith Frankston, Jeff Kahn, and Bhargav Narayanan.