### Thresholds versus fractional expectation-thresholds

- Series
- ACO Student Seminar
- Time
- Friday, December 6, 2019 - 13:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Jinyoung Park – Rutgers University

**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.