Visiting Assistant Professor
|Office||1019 Hylan Building|
|E-mail:||yxi4 at math dot rochester period edu|
- MW 3:30 - 4:30 pm
Courses I’m teaching this semester
Harmonic analysis: Kakeya-Nikodym problems, eigenfunction estimates, decoupling inequalities.
Publications and Preprints
On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets, (with S. Guo and T. Lan), preprint, arXiv:1911.10032.
Microlocal decoupling inequalities and the distance problem on Riemannian manifolds, (with A. Iosevich and B. Liu), preprint, arXiv:1909.05171.
ℓ^2 Decoupling in ℝ^2 for curves with vanishing curvature, (with C. Biswas, M. Gilula, L. Li and J. Schwend), preprint, arXiv:1812.04760, to appear in Proceedings of American Mathematical Society.
Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature, (with E. Wyman), preprint, arXiv:1807.00041.
Improved generalized periods estimates on Riemannian surfaces with nonpositive curvature, preprint, arXiv:1711.09864.
Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces, to appear in Journal of Geometric Analysis.
An endpoint version of uniform resolvent estimate for the Laplacian, (with T. Ren and C. Zhang), Forum Mathematicum, (2018) 30(5): 1279-1289.
On instability of the Nikodym maximal function bounds over Riemannian manifolds, (with C. D. Sogge and H. Xu), Journal of Geometric Analysis, (2018) 28(3): 28862901..
Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet Theorem, (with C. D. Sogge and C. Zhang), Cambridge Journal of Mathematics, (2017) 5: 123.
Improved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature, (with C. Zhang), Communications in Mathematical Physics, (2017) 350: 1299.
Bilinear Kakeya-Nikodym averages of eigenfunction on compact Riemannian surfaces, (with C. Miao, C. D. Sogge and J. Yang), Journal of Functional Analysis, (2016) 271: 2752.
On Kakeya-Nikodym maximal inequalities, Transaction of American Mathematical Society 369 (2017), 6351-6372.