The Convexity Conjecture, the Kahn-Kalai Conjecture, and introduction to k-thresholds

Series
Atlanta Combinatorics Colloquium
Time
Thursday, October 30, 2025 - 4:44am for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jinyoung Park – Courant Institute of Mathematical Sciences NYU – jinyoungpark@nyu.eduhttps://sites.google.com/view/jinyoungpark
Organizer
Tom Kelly

Please Note: Light refreshments will be offered before the talk at 4pm in the atrium.

The "Convexity Conjecture" by Talagrand asks (very roughly) whether one can "create convexity" in constant steps regardless of the dimension of the ambient space. Talagrand also suggested a discrete version of the Convexity Conjecture and called it "my lifetime favorite problem," offering $1,000 prize for its solution. We introduce a reformulation of the discrete Convexity Conjecture using the new notion of "k-thresholds," which is an extension of the traditional notion of thresholds, introduced by Talagrand. Some ongoing work on understanding k-thresholds, along with a (vague) connection between the Kahn-Kalai Conjecture and the discrete Convexity Conjecture, will also be discussed. Joint work with Michel Talagrand.