The ACO Seminar (2013–2014)

A partial result: if a planar curve intersects every line in at most 3 points, then it can be partitioned into 4 convex curves. This result can be extended to R^d, and the extension implies a good, asymptotically precise, lower bound on a geometric Ramsey number. Joint result with Jiří Matoušek and Attila Pór.