The APDE seminar on Monday, 2/10, will be given by Hannah Cairo (UC Berkeley) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Anuj Kumar (anujkumar@berkeley.edu).

Title: A Counterexample to the Mizohata-Takeuchi Conjecture

Abstract: We derive a family of $L^p$ estimates on the X-Ray transform of positive measures in ${\mathbb{R}}^d$, which we use to construct a $\log R$-loss counterexample to the Mizohata-Takeuchi conjecture for every $C^2$ hypersurface in ${\mathbb{R}}^d$ that does not lie in a hyperplane. In particular, endpoint multilinear restriction estimates cannot be derived from MT-type estimates.