The Mizohata-Takeuchi Conjecture predicts an $L^2$ estimate of functions with Fourier support on a convex hypersurface. It looks deceptively simple but remains a difficult problem to understand. I will talk about a recently found counterexample with Cairo showing power blowups for this conjecture for many hypersurfaces in all dimensions. Our construction was inspired by intuitions from additive combinatorics and lattice point counting for curves.
