Ruixiang.ZhangAffiliation: UC Berkeley Title Of Talk: The Mizohata-Takeuchi Conjecture for convex hypersurfaces Abstract: The Mizohata-Takeuchi Conjecture is a problem with PDE background. It 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.
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Last update made Tue Mar 10 21:28:06 CDT 2026.
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