Graduate Student / Postdoc Seminar

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

Speaker: Jinyoung Park, Courant Institute, New York University

Location: Warren Weaver Hall 1302

Date: Friday, November 7, 2025, 12:30 p.m.

Synopsis:

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.