Terence Tao on Nostr: Some progress in restriction theory: the Stein conjecture, a weighted L^2 version of ...

Some progress in restriction theory: the Stein conjecture, a weighted L^2 version of the restriction conjecture that would imply both the restriction and Kakeya conjectures, has shown by Hannah Cairo to be false (at least if no epsilon losses are allowed)! https://arxiv.org/abs/2502.06137 . In fact a slightly weaker, but still very interesting, version of the conjecture, known as the Mizohata-Takeuchi conjecture, was also been disproven. The counterexamples are concentrated near a lattice, and the failure is only by a logarithmic factor; so it is still possible that versions of this conjecture with "epsilon losses" are still true.

Incidentally, there will soon be an announcement of another major advance in this area (not by myself), but I cannot reveal the details at this stage. Stay tuned...