The ACO Seminar (2024–2025)

The Turan problem for hypercubes asks: how few vertices of the n-dimensional cube can we take so that they meet every d-dimensional subcube? A longstanding conjecture states that the best one can do (asymptotically) is 1/(d+1) of all vertices, by taking every (d+1)th layer of the cube. In this talk we will explain the connection to Turan questions for `daisy’ hypergraphs, and present a disproof of the conjecture. This is joint work with David Ellis and Maria Ivan.