A Counterexample to the Mizohata-Takeuchi Conjecture An In-Depth Analysis of Hannah Cairo's Breakthrough Discovery

Preface

In February 2025, mathematician Hannah Cairo published a groundbreaking result that fundamentally altered our understanding of weighted Fourier extension estimates. Her work demonstrated that the Mizohata-Takeuchi conjecture-a central problem in harmonic analysis that had stood for decades is false, albeit with only logarithmic losses. This discovery has profound implications not only for the conjecture itself but for the entire landscape of Fourier restriction theory.

This e-book provides a comprehensive examination of Cairo's discovery, contextualizing it within the broader field of harmonic analysis while making the technical content accessible to graduate students and researchers across mathematical disciplines.