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I am a postdoctoral fellow at Courant Institute of Mathematical Sciences. I did my Ph.D. under the advise of
Terry Tao
at the
UCLA Department of
Mathematics. My research interests include
non-linear dispersive and wave PDE,
real-variable harmonic
analysis (oscillatory integrals in particular), and applications of
infinite
dimensional Hamiltonian dynamics in PDE.
This webpage is not regularly updated. Sorry!
Curriculum Vitae
- Global well-posedness of the cubic nonlinear Schr\"odinger equation on compact manifolds without boundary. (submitted) arXiv:1008.2826v1.
-
A bilinear oscillatory integral estimate and bilinear refinements to Strichartz estimates on closed manifolds (submitted) arXiv:1008.2827v1.
- Global and dynamical aspects of the nonlinear Schr\"odinger equations on compact manifolds. Ph.D Thesis.
- Expository Notes:
- Most of these
notes were loosely written to accompany talks at the UCLA
participating analysis
seminar.
- Discrete and continuous parametrices for variable coefficient wave and Schr\"odinger equations (PDF)
- Bourgain's Fourier Truncation (or high-low) method (Fall 2009) (PDF)
- Some Scattering Aspects for NLS in Periodic and Non-periodic Regimes (Spring 2009) (PDF)
- Notes on
the Classical KAM theory (Winter 2009) (PDF)
- Strichartz
Estimates on Tori [after
J. Bourgain's Fourier Restriction Phenomena... Part I] (Fall 2008)