My research interests are Dispersive Partial Differential Equations and Harmonic Analysis. I study the long-time behavior (global well-posedness and scattering) of dispersive equations via deterministic and probabilistic methods. 

My results can be found on arXiv.

• Global well-posedness and scattering for the defocusing mass-critical Schr\"odinger equation in the three-dimensional hyperbolic space,

with Bobby Wilson, [arXiv: 2310.12277].

• On scattering for critical NLS on waveguide manifolds: a short survey,

with Zehua Zhao.

• On Strichartz estimates for many-body Schr\"odinger equation in the periodic setting,

with Zehua Zhao and Jiqiang Zheng, [arXiv:2304.00882].

• On recovering the nonlinearity for generalized higher-order Schr\"odinger equations*,

with Zachary Lee, [arXiv: 2303.06312] [Inverse Problems and Imaging].

• On well-posedness results for the cubic-quintic NLS on $\mathbb{T}^3$,

with Yongming Luo, Haitian Yue, and Zehua Zhao, [arXiv:2301.13433].

• On the uniqueness of variable coefficient Schr\"odinger equations,

with Zongyuan Li and Serena Federico, [arXiv: 2211.03740].

• On uniqueness properties of solutions of the generalized fourth-order Schr\"odinger equations*,

with Zachary Lee, [arXiv: 2208.07355].

• Modified scattering of cubic nonlinear Schr\"odinger equation on rescaled waveguide manifolds, 

with Bobby Wilson, [arXiv: 2207.07248].

• Singular Levy processes and dispersive effects of generalized Schr\"odinger equations, 

with Yannick Sire, Haitian Yue, and Zehua Zhao, [arXiv: 2207.00485] [Dynamics of PDE].

• On the decay property of the cubic fourth-order Schr\"odinger equation, 

with Haitian Yue and Zehua Zhao, [arXiv: 2201.00515] [Proceedings of the AMS].

• Global well-posedness and scattering for fourth-order Schr\"odinger equations on waveguide manifolds, 

with Haitian Yue and Zehua Zhao, [arXiv: 2111.09651].

• Global well-posedness and long-time behavior of the fractional NLS,  

with Mouhamadou Sy, [arXiv: 2011.13904] [SPDE: Analysis and Computations].

• On the global well-posedness for the periodic quintic nonlinear Schr\"odinger equation, 

with Haitian Yue, [arXiv: 2011.12925].

• Global well-posedness for the cubic fractional NLS on the unit disk, 

with Mouhamadou Sy, [arXiv: 2011.05517] [Nonlinearity]. 

• Global well-posedness for the focusing cubic NLS on the product space $\mathbb{R} \times \mathbb{T}^3$,  

with Haitian Yue and Zehua Zhao, [arXiv: 2009.01116] [SIAM Journal on Mathematical Analysis].

• Almost sure global well-posedness for NLS on the unit ball of $\mathbb{R}^3$, 

with Mouhamadou Sy, [arXiv: 2007.00766].

• On the high-low method for NLS on the hyperbolic space, 

with Gigliola Staffilani, [arXiv: 2004.05711] [Journal of Mathematical Physics] (Special Collection: Celebrating the work of Jean Bourgain).

• Global well-posedness and scattering for the defocusing quintic nonlinear Schr\"odinger equation in two dimensions,

[Doctoral Dissertations].

• Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schr\"odinger equation in $\mathbb{R}^2$,

[arXiv: 1805.03230] [Analysis & PDE].

*Projects involving undergrads

• Recent Developments and Future Directions in Nonlinear Dispersive and Wave Equations, Monash University, Australia, December 2023

• Analysis Seminar, Oregon State University, November 2023

• Analysis Seminar, University of Oregon, November 2023

• Differential Geometry/PDE Seminar, University of Washington, May 2023

• Analysis Seminar, University of Massachusetts Amherst, April 2023

• Early Career Math Colloquium in the Department of Mathematics, University of Arizona, April 2023

• Special Session "Dynamics of Partial Differential Equations", AMS Sectional Meeting, March 2023

• Workshop on "Women in nonlinear dispersive PDEs", Banff, February 2023

• Online Analysis Research Seminar, September 2022

• Analysis Seminar, Academy of Mathematics and Systems Science, CAS, September 2022

• Minisymposium "Recent Advances in Mathematical Fluid Mechanics", SIAM Pacific Northwest Conference at Washington State University Vancouver, May 2022

• Analysis and PDE Seminar, University of North Carolina at Chapel Hill, April 2022

• Rainwater Seminar, University of Washington, February 2022

• Colloquium, Oregon State University, February 2022

• Analysis and PDE Seminar via Zoom, Beijing Institute of Technology, China, November 2021

• Analysis Seminar, Brown University, November 2021

• The 17th Prairie Analysis Seminar, Kansas State University, November 2021

• Workshop on "Generic Behavior of Dispersive Solutions and Wave Turbulence", ICERM, October 2021

• Ghent Methusalem Junior Seminar via Zoom, Belgium, September 2021

• Special Session "Deterministic and Probabilistic Aspects of Nonlinear Evolution Equations", Mathematical Congress of the Americas, July 2021

• Special Session "Probabilistic Methods in Partial Differential Equations", Joint Mathematics Meetings, January 2021

• PDE/Analysis Seminar, MIT, March 2020

• HAPDE Seminar, University of Virginia, February 2020

• APDE Seminar, Basque Center for Applied Mathematics, Spain, January 2020

• Analysis Seminar, University of Massachusetts Amherst, November 2019

• Workshop for Northeast Women in PDE and Applied Math, University of Connecticut, October 2019

• FRG Conference, University of Chicago, October 2018

• PDE and Differential Geometry Seminar, University of Connecticut, October 2018

• PDE/Analysis Seminar, MIT, September 2018

• Boston University/Keio University Workshop: Dynamical Systems, Boston University, June 2018

• Advancing Women’s Impact in Mathematics, New England (AWIMS), Worcester Polytechnic Institute, April 2018

• FRG-NSF Women in PDE mini-conference, University of Massachusetts Amherst, March 2018

• Second Northeastern Analysis Meeting (NEAM 2017), University at Albany, SUNY, October 2017