12 citations · 20 across the 7 of their papers we have counts for
7 papers
Power loss for the Mizohata-Takeuchi conjecture on convex hypersurfaces
Hannah Cairo, Ruixiang Zhang
We find a family of compact hypersurfaces where the local Mizohata-Takeuchi Conjecture fails with a power loss of for any . Moreover, this family i…
Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics
Wencai Liu, Matthew Powell, Yiding Max Tang +3
We establish asymptotically sharp semi-algebraic discrepancy estimates for multi-frequency shift sequences. As an application, we obtain novel upper bounds for the quantum dynamics…
The Brascamp-Lieb inequality and its influence on Fourier analysis
Ruixiang Zhang
Brascamp-Lieb inequalities have been important in analysis, mathematical physics and neighboring areas. Recently, these inequalities have had a deep influence on Fourier analysis a…
Improved bounds for the Kakeya maximal conjecture in higher dimensions
Jonathan Hickman, Keith M. Rogers, Ruixiang Zhang
We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to the context of the Kakeya problem. By writing out the induction argument as a recursive algo…
Polynomials with dense zero sets and discrete models of the Kakeya conjecture and the Furstenberg set problem
Ruixiang Zhang
We prove the discrete analogue of Kakeya conjecture over . This result suggests that a (hypothetically) low dimensional Kakeya set cannot be constructed directly from…
On sharp local turns of planar polynomials
Ruixiang Zhang
We show that for a real polynomial of degree in two variables and , any local "sharp turn" must have its "size" . We also show that there is indeed…
On configurations where the Loomis-Whitney inequality is nearly sharp and applications to the Furstenberg set problem
Ruixiang Zhang
In this paper, we consider the so-called "Furstenberg set problem" in high dimensions. First, following Wolff's work on the two dimensional real case, we provide "reasonable" upper…