MIT-Harvard-MSR Combinatorics Seminar: Threshold for Steiner triple systems

Name: MIT-Harvard-MSR Combinatorics Seminar: Threshold for Steiner triple systems
Start: 2022-04-20T16:15:00-04:00
End: 2022-04-20T17:15:00-04:00
Location: MIT, Room 2-139

When: April 20, 2022

4:15 pm - 5:15 pm

Where: MIT, Room 2-139

Speaker: Mehtaab Sawhney - MIT

We prove that with high probability $G^{(3)}(n,n^{-1+o(1)})$ contains a spanning Steiner triple system. We also prove the analogous result for spanning Latin squares. This threshold is sharp up to a subpolynomial factor. Our result follows from a novel bootstrapping scheme that utilizes iterative absorption as well as recent connections which have been established between thresholds and spread measures. Joint work with Ashwin Sah and Michael Simkin.