Yakun Xi
Visiting Assistant Professor
Office  1019 Hylan Building 
Phone:  (585) 2754419 
Fax:  (585) 2734655 
Email:  yxi4 at math dot rochester period edu 
Office hours
 MW 3:30  4:30 pm
Courses Iām teaching this semester
Research Interest
Harmonic analysis: KakeyaNikodym problems, eigenfunction estimates, decoupling inequalities.
Publications and Preprints

On Convexity, MidPoint 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.

ā^2 Decoupling in ā^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): 12791289.

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 GaussBonnet 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 KakeyaNikodym averages of eigenfunction on compact Riemannian surfaces, (with C. Miao, C. D. Sogge and J. Yang), Journal of Functional Analysis, (2016) 271: 2752.

On KakeyaNikodym maximal inequalities, Transaction of American Mathematical Society 369 (2017), 63516372.