ICM 2026: A Magical Saturday Afternoon with Park, Braden and Proudfoot, and Meka

Saturday afternoon, July 25, was quite magical for me: all three beautiful talks were closely related to my interests and to my own work. Here is a brief personal description of the lectures, with links to the slides and papers, followed by a more detailed account of each talk. Jinyoung Park gave a beautiful talk entitled “Thresholds,” concerning an array of conjectures about the location of thresholds for monotone properties and some of their applications. She concentrated on three conjectures: the Kahn–Kalai conjecture, also known as the expectation-threshold conjecture; the second Kahn–Kalai conjecture; and Talagrand’s discrete convexity conjecture. Here are the links to the proceedings paper and the slides. Tom Braden and Nicholas Proudfoot gave a beautiful talk entitled “Intersection Cohomology Without Spaces,” devoted to a major theme in algebraic combinatorics: geometric structures can survive, and remain powerful, even in settings where the geometry itself does not exist. They…