Talagrand’s discrete-convexity conjecture
We prove Talagrand's discrete-convexity conjecture. There is a universal integer k such that, whenever an arbitrary family has Bernoulli product measure at least $1-1/k$, the sets not contained in a union of k members admit a cover of total cost at most 1/2 at the same density.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
reports proofs of the second Kahn–Kalai conjecture , which bounds graph-containment thresholds using subgraph expectations, and of Talagrand’s discrete convexity conjecture , both discussed in my account of Jinyoung Park’s ICM lecture . A companion result makes integral and fractional expectation…