My advisor is Daniel Tataru

*A sharp upper bound on the range of Sobolev exponents for which the NLS and NLW equations admit solutions*, joint with Mitchell Taylor, in preparation.*Low regularity solutions for the general quasilinear ultrahyperbolic Schrödinger equation*, joint with Mitchell Taylor. arXiv:2310.19221 [math.AP]*Sharp Hadamard local well-posedness, enhanced uniqueness, and pointwise continuation criterion for the incompressible free boundary Euler equations*, joint with Mihaela Ifrim, Daniel Tataru, and Mitchell Taylor. arXiv:2309.05625 [math.AP]*Stable phase retrieval in function spaces*, joint with Daniel Freeman, Timur Oikhberg, and Mitchell Taylor, accepted in**Math. Ann.**arXiv:2210.05114 [math.FA]*Examples of Hölder-Stable Phase Retrieval*, joint with Michael Christ and Mitchell Taylor, accepted in**Math. Res. Lett.**arXiv:2205.00187 [math.CA]*Global well-posedness for the generalized derivative nonlinear Schrödinger equation*, joint with Mitchell Taylor. arXiv:2112.04648 [math.AP]*No pure capillary solitary waves exist in 2D finite depth*, joint with Mihaela Ifrim, Daniel Tataru and Mitchell Taylor, accepted in**SIAM J. Math. Anal.**arXiv:2104.07845 [math.AP]*New Regularity Criteria for the Navier-Stokes Equations in Terms of Pressure*, joint with Xinwei Yu. arXiv:1910.08911 [math.AP]*On Prodi–Serrin type conditions for the 3D Navier–Stokes equations*, joint with Xinwei Yu,**Nonlinear Analysis Theory Methods and Applications**. Vol. 190, (2020). link*A New Prodi–Serrin Type Regularity Criterion in Velocity Directions*, joint with Xinwei Yu,**Journal of Mathematical Fluid Mechanics**. Vol. 20, pages 1737–1744 (2018). link

*Invited speaker at conference on lattice problems in analysis*. May, 2024 (Tentatively). ICMAT, Madrid, Spain.*UCLA Analysis and PDE seminar*. November 28th, 2023. UCLA, Los Angeles, CA, USA.*Oberwolfach seminar: Scattering Resonances in Quantum Mechanics, General Relativity and Hyperbolic Dynamics . November, 2023. Oberwolfach, Germany.**ETH Zurich Analysis seminar. Nov. 14th, 2023. ETH, Zurich, Switzerland.**UC Berkeley Analysis and PDE seminar. Sept. 25th, 2023. UC Berkeley, Berkeley, CA, USA.**MSRI, FD2 Reunion seminar. August 10th, 2023. Simons Laufer Mathematical Sciences Institute, Berkeley, CA, USA.**Wisconsin PDE seminar. April. 24th, 2023. University of Wisconsin–Madison, Madison, WI, USA.**ICMAT PDE’s and Fluid Mechanics seminar*. Nov. 3rd, 2022. ICMAT, Madrid, Spain.*Oberwolfach seminar: Free Boundary Problems in Fluid Dynamics . October, 2022. Oberwolfach, Germany.**Harmonic Analysis and Differential Equations Seminar (HADES)*. May 10th, 2022. UC Berkeley, Berkeley, CA, USA.*PDE Learning Seminar (Fall 2021) Nonlinear wave equations and general relativity*. Nov. 3rd, 2021; via Zoom. UC Berkeley, Berkeley, CA, USA.*Harmonic Analysis and Differential Equations Seminar (HADES)*. Oct. 26th, 2021. UC Berkeley, Berkeley, CA, USA.*MSRI, Mathematical problems in fluid dynamics graduate student working group*. May. 12th, 2021; via Zoom. MSRI, CA, USA.*Seminar on wave packets in dispersive PDE*. Nov. 17th, 2020; via Zoom. UC Berkeley, Berkeley, CA, USA.*Seminar on singularity formation for incompressible Euler*. Mar, 2020. UC Berkeley, Berkeley, CA, USA.*Harmonic Analysis and Differential Equations Seminar (HADES)*. Nov. 19th, 2019. UC Berkeley, Berkeley, CA, USA.*The XI Americas Conference on Differential Equations and Nonlinear Analysis*. August 19, 2017, University of Alberta, Edmonton, Canada.