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I am interested in the interplay between harmonic analysis and partial differential equations, as well as their interactions with other fields.   

• Harmonic analysis

to study the boundedness in various function spaces of many linear/multilinear operators related to the Fourier restriction problems and PDE,  space-time estimates for dispersive equations,  adaptive function spaces and analysis tools associated to operators and PDE

• Nonlinear partial differential equation

to study the nonlinear evolutionary PDE arising in mathematical physics such as nonlinear dispersive equations, Navier-Stokes equation.  Main concerns are the low-regularity local/global well-posedness theory, long-time/blow-up behavior of the solution, stability of the equation, playing tools from many other areas including harmonic analysis, functional analysis, ODE and probability, etc.

The topics of the PhD project relate to the interplay between harmonic analysis and nonlinear dispersive equations. The study of dispersive PDE has been greatly transformed by the integration of harmonic analysis thinking and technology. On the other hand, dispersive PDE are a powerful source of harmonic analysis questions with real physical significance.

1) to develop the most recent linear and non-linear harmonic analysis method

2) to adapt the newly developed methods to problems in nonlinear dispersive equations, e.g., well-posedness, asymptotic behaviour. 

Candidates are expected to have finished, or be about to finish, a Master's degree in mathematics or an equivalent qualification (candidates with degrees on different disciplines must show evidence that they completed a sufficient amount of mathematical training). A good command of measure theory, functional analysis, Fourier analysis, and PDEs is required.

Please feel free to contact me and introduce yourself with 1) CV; 2) Transcripts; 3) English results (optional); 4) Other documents (optional), e.g., publications, certificate.